COCOA BRIOCHE MORNING BUNS

Steps:

• Pre-ferment
• Mix flour, milk, and yeast in the bowl of a stand mixer until combined (mixture will be thin, like a batter). Let rise, uncovered, in a warm spot until doubled in size, about 1 hour.
• Dough
• Add egg, milk, and yeast to pre-ferment and attach to stand mixer. Fit with dough hook and beat on low speed until combined. Add granulated sugar, cocoa powder, salt, 5½ cups (687 g) all-purpose flour, and 2 Tbsp. room-temperature butter; mix on low speed until a smooth dough forms. Transfer dough to a large bowl, cover with a damp kitchen towel, and let rise in a warm spot until doubled in size, about 1 hour.
• Meanwhile, mix 2¼ cups (4¼ sticks) cool butter in the clean bowl of a stand mixer with paddle attachment on low speed until smooth and spreadable but still cool. Turn out onto a sheet of parchment paper and shape butter into a small rectangle with an offset spatula. Cover with another sheet of parchment paper and roll out butter to a 16x12" rectangle. Chill butter until dough is ready (you want to keep butter cool but malleable; don't let it get too firm).
• Turn dough out onto a generously floured work surface and roll into a 24x12" rectangle; position with a short side facing you. Uncover butter and place on top of dough, lining it up along near edge and covering bottom two thirds of dough. Fold top third of dough up and over butter, then fold bottom third up and over (like a letter). Quickly, but gently, roll out dough again to a 24x12" rectangle, flouring work surface and rolling pin as needed to avoid sticking. (If at any point dough gets too sticky to handle or butter is starting to melt, chill in fridge 20 minutes and let firm up before proceeding.) Fold dough into thirds again, wrap in wax paper or plastic, and chill 1 hour.
• Remove dough from fridge and repeat rolling and folding as above, one more time. Cut folded dough into 3 equal rectangles and wrap each tightly in plastic. Chill until ready to use. Do ahead: Dough can be made 1 day ahead. Keep chilled, or freeze up to 2 months.
• Filling and assembly
• When you're ready to bake buns, generously butter the cups of a 6-cup jumbo muffin pan; sprinkle each cup generously with raw sugar. Mix together brown sugar, cinnamon, salt, and ⅓ cup (66 g) granulated sugar in a small bowl.
• Working with 1 piece of dough, unwrap and roll to a 12x6" rectangle about ¾" thick. Cut into six 6x2" rectangles. Starting ¼" from top of a short side, cut 2 lengthwise slits in a rectangle of dough to create 3 equal strands. Braid strands and sprinkle generously with brown sugar mixture. Lay 2 or 3 small pieces of chocolate on braid and coil, stacking up onto itself. Place bun, braid side up, in prepared muffin pan. Repeat with remaining 5 rectangles. You will want to use a third of the brown sugar mixture and a third of the chocolate, reserving the remaining brown sugar mixture and chocolate for the remaining 2 pieces of dough.
• Preheat oven to 375°. Loosely cover buns with a kitchen towel or plastic wrap and let rise until a little less than doubled in size, about 30 minutes. (Alternatively, let buns rise in fridge overnight and bake in the morning. If buns have not risen noticeably in fridge, let sit at room temperature 30-60 minutes before baking.)
• Whisk egg and 2 tsp. water in a small bowl. Brush tops of buns with egg wash and bake until tops are puffed and have developed a crisp outer layer, about 35 minutes. (Unmolded buns should sound slightly hollow when tapped.) Let cool in pan 2 minutes, then gently lift out of pan and transfer to a wire rack. Let sit until buns are cool enough to handle.
• Place some granulated sugar in a medium bowl. Working one at a time, toss buns in sugar and return to rack. Let cool completely. Repeat with remaining pieces of dough, or save remaining cinnamon mixture and chocolate pieces separately in airtight containers at room temperature until ready to bake remaining dough. Do ahead: Buns can be baked 1 day ahead. Store airtight at room temperature.