See the photo gallery below for target dough consistency and rise.
These instructions are for using a stand mixer, but hand mixing is fine. To add the chocolate chips by hand, I suggest lamination about 15 minutes after the initial mixing.
Mixing and First Rise
In the bowl of a stand mixer, whisk the flours, salt, yeast, and spices. If you'd like to bloom the yeast, add it to the liquid (next step) when it is under 110°F.
Heat the milk until it is warm then stir in the butter pieces and brown sugar to melt/dissolve.
Add the warm milk-butter-sugar mixture and the egg to the dry ingredients and mix with the dough hook on low speed, adding as much of the 80 grams of water as is needed for the dough hydration to be slightly sticky but not stay on your fingers when you touch it. The dough should be wrapped around the hook.
Mix for 2-3 minutes, add the chocolate chips and mix another minute, or use your hands to knead and fold the chips into the dough.
Transfer the dough to a bowl or straight-walled bucket, cover, and let rise until it has has expanded by 75-100%. Depending on your dough/ambient temp, this may take 1-2 hours.
Shaping and Final Proof
Grease a 9" x 9" square pan or line it with parchment paper.
Place the dough on a clean work surface, gently de-gas it, and divide into nine pieces.
Roll the pieces into balls and place them in your pan.
Cover and let rise until doubled, around 1-2 hours.
Icing, Baking, and Glazing
Preheat your oven to 350°F.
For the piped crosses, melt the chocolate chips with the milk in a glass bowl or Pyrex in the microwave (15-20 seconds, mix/check on the progress, repeat until melted). Mix in the flour and spoon the paste into a small plastic bag.
Cut a ⅛" hole in one corner of the bag and pipe horizontal and vertical lines onto the fully proofed buns. For thicker lines, make double the icing and cut a ¼" hole in the bag.
Bake the buns for 28 minutes or until the internal temperature of the center bun is over 190°F.
Remove the pan from the oven and set it on a towel or cooling rack.
Combine the sugar and water for the glaze then heat briefly in the microwave to dissolve the sugar. Brush the glaze on the warm buns and serve warm.
The buns can be stored at room temperature in a sealed container or covered with plastic for several days. Reheat each bun for 10-15 seconds in the microwave to soften before serving. To freeze, wrap each bun tightly with plastic wrap.
