In a large bowl, mix together 150 grams flour with sugar and salt.
Cut the cold, unsalted butter into small chunks (about 16 pieces per stick of butter) and add to the flour mixture. Using a pastry cutter, cut the butter into the flour mixture until all of the butter is moistened by the flour and forms into a thick paste (see pictures in the recipe post). Alternatively you can grate the cold butter into small flakes and incorporate them into a thick paste.
Add the remaining 175 grams (1 ¼ cup) of flour and use the pastry cutter or your fingers to distribute the flour until the mixture looks crumbly.
Pour the chilled sourdough discard on top of the flour/butter mixture and stir to combine. Use your hands to form the dough into a ball. If the dough is too crumbly, add ice cold water a Tablespoon at time until it comes together.
Cut the ball in half and form two balls of dough. Set one ball of dough to the side. Preheat the oven to 350ºF.Note: At this point the dough will still be chilled from the cold ingredients. If it warms up, refrigerate it for 15-20 minutes to chill.
Flour the countertop and place the ball of dough on top of the flour. Roll one section of dough out into a 9 by 12-inch rectangle, flouring as needed so the dough doesn't stick to the rolling pin. I roll the dough a little bit large and then use a bench scraper or pizza cutter to cut the dough into a 9 by 12-inch rectangle. Repeat with the other portion of dough so you have two 9 by 12-inch rectangles.
Use the bench scraper to mark the dough every three inches (on the 9-inch side) and every four inches (12-inch side). Use a pizza cutter to cut each rectangle into 9 equal-sized smaller rectangles, 3 by 4-inches each. Place 9 rectangles of dough on a parchment-lined baking sheet.
Whisk together egg with a splash of water. Brush egg wash on top of each rectangle of dough.
Spoon about 1 - 1 ½ Tablespoons jam into the center of each pop tart. Place a rectangle of dough on top of the jam filling, sandwiching the pop tart together. Crimp and seal the edges with a fork, by pressing down on the edges all the way around the pop tart. Repeat with remaining dough rectangles until all the pop tarts are sealed. Brush with egg wash.Note: If you add too much filling or don't crimp enough, the filling can leak out, so be careful not to over-fill. If you do, the jam can easily be brushed away from the baked pop tarts. Before adding the egg wash pop tarts can be frozen to be baked later if desired.
Bake at 350ºF for about 30 minutes until light brown, flaky and puffed up. Remove from the oven and let cool while you whisk up the glaze.
Glaze: Whisk together powdered sugar, milk, vanilla extract, and a pinch of salt. If you want the glaze a little more thick, add a little extra powdered sugar. To thin it out add a little extra milk. I love using vanilla bean paste in place of vanilla extract if you can find it. Spoon glaze on top of slightly cooled pop tarts and let cool before enjoying!
