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Step 1
Combine one tablespoon of sugar (from the ¼ cup), yeast, and warm milk in the bowl of a stand mixer to bloom for 5 minutes. Once foamy, add the remaining sugar, egg and yolk, flour, and salt. Using the dough hook attachment, mix on medium speed until it comes together into a shaggy ball.
Step 2
Turn the speed one click lower, then add 1 tablespoon of the softened butter at a time. Wait to add the next piece of butter until the prior piece is mostly incorporated.
Step 3
Mix on medium high speed until the dough is totally smooth, scraping down the sides and bottoms a few times. If the dough hasn't turned smooth, increase the speed and keep mixing. It will come together!
Step 4
When it’s ready, the dough should completely be pulled away from the sides and mostly or fully off of the bottom. If a bit is still sticking to the bottom of the bowl, just pull it off. The dough will be very soft and supple when it’s ready.
Step 5
Form the dough into a ball and place the dough in an oiled bowl, cover with plastic wrap, and refrigerate for 8 hours or overnight. The dough won’t look like it rose very much, which is normal!
Step 6
Chop the chocolate, then melt the butter and chocolate together in 30 second bursts in the microwave, stirring in between each, until smooth. Add the powdered sugar, cocoa powder, and espresso powder and mix until it forms a paste.
Step 7
Prepare a standard loaf pan with a strip of parchment paper overhangs and set side.
Step 8
Lightly flour your work surface and rolling pin, shape the dough into a rectangle with your hands, then roll the dough out into a roughly 10x14 inch rectangle. Push the dough down a few times with your rolling pin to begin to flatten, then roll. Use a bench scraper to keep the dough in a rectangle shape.
Step 9
Once rolled out, make the filling, then immediately spread it over the dough with an offset spatula. Leave a 1/2 inch border on all sides except for one of the long edges (this will be where you start the initial roll). Work quickly, and spread it as evenly as possible.
Step 10
Starting from the long edge where the filling meets the edge, tightly and evenly roll the dough into a log. Pinch the long edge of the dough into the roll the whole way across, and then place that side down to keep the seal.
Step 11
Transfer the dough to a parchment lined baking sheet and gently push the dough together from each side, just to re-compact the log a bit.
Step 12
Cut off the edge of each side of the log - about an inch (which is what you didn’t cover with filling). Then, cut the entire log in half lengthwise and place each piece in line with each other so the filling side is up.
Step 13
Pinch the top edges together as best as possible, then, keeping the cut sides up, twist each piece of dough around each other as many times as possible, then pinch to seal the bottom edge. This part may not look perfect, but the key is to keep the cut sides UP as best as possible.
Step 14
Place the dough in the prepared loaf pan. If it's too long to fit in, just tuck one of the edges next to it like an “s”.
Step 15
Cover the dough with plastic wrap and allow it to rise in a slightly warm location for about 1-2 hours until the dough puffs up and starts to fill out the pan a bit. If your kitchen is rather cold, try another room in the house, or allow it to rise in a closed oven (no heat) with just the light on.
Step 16
Preheat the oven to 375°F/190℃, uncover the loaf, and bake for 25-30 minutes in the middle rack. You’ll know it’s done when you can insert a sharp knife and it has little resistance. If it still feels at all stretchy or doughy when you poke it in, allow it to bake for another 3-5 minutes and check again.
Step 17
As soon as the babka goes into the oven, make the simple syrup. Add the water, sugar, and espresso powder in a small saucepan and heat and stir until the sugar dissolves, then cool completely.
Step 18
As soon as the babka comes out of the oven, brush or spoon the simple syrup over the top, getting every nook, cranny, and edge, until it’s gone. It may feel like too much syrup, but it’s not!
Step 19
Cool until warm, then slice and enjoy.