In a stand mixer bowl with a dough hook attachment, add in the water, soy milk, yeast, Just Egg, softened butter, flour, sugar, and kosher salt (if using unsalted butter). Mix on low for 2 minutes or until ingredients are incorporated, scraping the sides and bottom as necessary. Increase speed to medium-low and mix until a smooth, soft dough forms. This should take about 8-10 minutes.If the dough is too sticky and continues to stick to the sides and bottom of the bowl, add in flour one tbsp at a time, allowing the flour to fully incorporate into the dough before adding another. The dough should be tacky but not overly sticky.

Lightly sprinkle flour on the bottom of a large bowl. Remove the dough from the stand mixer, form it into a ball, and transfer it to the floured bowl. Tightly cover with plastic wrap. Let rise until doubled in size (about 1 hour).

Once the dough has doubled in size, lightly punch down the dough with your fist. Lay out two pieces of plastic wrap, one vertical and one horiztonal, so that they overlap in the center, forming a cross. Place the dough in the center of the plastic wrap. Fold the plastic wrap pieces over the dough in a square shape so that you make a neat square packet. Flip the square packet over so it is seam-side down. Use a rolling pin to work the dough to create an even layer of dough. The dough should fully fill the plastic wrap square, including the corners.Place the dough in the fridge for at least 2 hours and up to 16 hours. A longer rest will result in a better end result.

Cut the remaining butter into small pieces. Place the butter pieces in the middle of a sheet of parchment paper (about 20" x 15") so that they form a 7" x 7" square. You may not have enough butter pieces to completely fill the square, but make sure you complete the perimeter of the square. Fold the pachment paper tightly around the perimeter of the butter square to form a neat 7" x 7" square packet.It is better to make the initial butter square slightly smaller than 7" x 7", maybe about 6.5" x 6.5", to account for the butter spread slightly in the next step. However, try to get the final butter block as close to 7" x 7" as possible.

Flip the butter packet so it is seam-side down. Use a rolling pin to gently and firmly roll out the butter to create an even block of butter. The butter block should fully fill the parchment packet, including the corners. Place the wrapped butter block in the fridge until 10 minutes before you are ready to laminate the dough.

10 minutes before you plan to take the dough out of the fridge, move the wrapped butter block from the fridge to the freezer.

Remove the dough from the fridge, unwrap it, and place it on a lightly floured surface. Roll out the dough into an 10" x 10" square. Remove the butter block from the freezer, unwrap it, and place it in a diamond position on top of and in the center of the dough.

One corner at a time, fold the corners of the dough in towards the center of the butter block. The dough corners should overlap. Pinch along the overlapping seams. The butter block should be completely enclosed in the dough.

In our experience, since vegan butter is typically not as firm as non-vegan butters the butter might start becoming soft. If that is the case, wrap the dough in plastic wrap and place it in the freezer for 10 minutes to give the butter time to firm up before continuing.

Flip the dough so it is seam-side down. Lightly flour the top and bottom of the dough. Use a rolling pin to gently press down along the length of the top of the dough to create little indents in the dough. Turn the dough 90º and gently press down along the length of the dough again. The goal here is to make the butter inside the dough a little more pliable so it is easier to roll.

Roll out the dough into a rectangle that is roughly three times longer than it is wide, dusting more flour as needed and occasionally moving the dough to ensure it doesn't stick to the surface. Make sure to roll both towards you and away from you to ensure the butter is evenly distributed inside the dough. Roll until the dough is between ¼ inch and ½ inch thick.

Fold the dough into thirds like a letter by lifting one end (a third of the dough) of the rectangle up onto the center of the dough, followed by the other end of the rectangle. The resulting dough will be three layers stacked on top of each other. This is your first "turn" of the dough.Again, if you think your butter is becoming soft, wrap the dough in plastic and place it in the freezer for 10 minutes.

Rotate the dough 90º. (If you placed your dough in the fridge after the first "turn", make sure the flap is on the top of the dough and the edge of the flap is on the right.) Repeat the rolling and folding process. This is your second "turn".Wrap and chill again, if necessary.

Rotate the dough 90º a final time. (Again, if you placed your dough in the fridge, make sure the flap is on the top of the dough and the edge of the flap is on the right.) Repeat the rolling and folding process. This is your third and final "turn".

Wrap the dough in plastic wrap and place it in the fridge. Let it rest for 1 hour.

Line two baking sheets with parchment paper.

Remove the dough from the fridge, unwrap, and place on a lightly floured surface. Roll out the dough into a square slightly larger than 14" x 14". Trim the edges of the dough so you have a neat 14" x 14" square, and discard the scraps.

Cut the dough into 16 squares (4 x 4 grid) that measure 3.5" x 3.5". Transfer the squares to the baking sheets.

For each dough square, fold the corners of the dough in toward the middle of the square. Press the corners down into the dough so that they stay in place. You can wet your finger to help the corners stay down.

Loosely cover the baking sheets with plastic wrap. Let rise until the dough is puffed, about 1 hour.

Position oven racks on the top and bottom thirds of the oven. Preheat the oven to 400ºF.

In a small mixing bowl, combine all of the filling ingredients and mix until well-combined. Try to get rid of any lumps, but some lumps are fine.

Uncover the baking trays. Use your thumb to press down on the center of each piece of dough to create a small well, fixing any of the pressed down corners that may have come undone. Place a heaping 1 tbsp of filling on the center of each piece of dough.You can also fill with your favorite fruit jam or mix and match cream cheese and jam. Try to keep the filling amount to about 1½ tbsp.

In a small bowl or glass, combine the ingredients for the brushing liquid and mix until well-combined. Use a pastry dough to brush the tops of the dough with the mixture.

Place one baking tray on the top rack and one on the bottom rack. Bake for 15-20 minutes or until the pastries are a deep golden brown, switching the two baking trays after 10 minutes.

Remove the baking sheet from the oven. Let cool for 5 minutes on the trays, then transfer pastries to a wire rack. Let cool for another 30 minutes to allow the fillings to set.

In a small mixing bowl, combine all of the drizzle ingredients and mix until well-combined. Add more powdered sugar or milk (in very small quantities) to get a drizzle consistency.

Use a piping bag, plastic bag with the corner snipped off, or just a spoon to drizzle the mixture on the tops of the pastries.