In a 4-cup measuring cup or medium bowl, stir together the milk and yeast and let sit for 5 minutes. Then, whisk in the sugar, egg, and egg yolk.
In the bowl of an electric mixer fitted with the dough hook, add the flour and salt. Mix on low speed to combine, about 1 minute. Add the yeast mixture and mix until most of the flour has been incorporated, about 1 minute.
Add the butter a few chunks at a time and knead until the dough forms a soft, smooth dough that is just slightly sticky when squeezed together, about 5 to 10 minutes. Turn the dough out onto a lightly floured surface and knead just a few times until the dough is smooth, then place in a greased bowl, turning to coat the dough. Cover with plastic wrap and place in a warm, draft-free spot to rise until doubled in size, about 1 hour.
Make the Chocolate Filling
In a large bowl, stir together the chopped chocolate, sugar, and cinnamon. Add the butter and, using a pastry blender or a fork, cut the butter into the mixture until completely combined.
Make the Egg Wash
In a small bowl, whisk together the egg and heavy cream.
Assemble the Babka
Grease two 9x5-inch loaf pans with butter, then line with parchment paper; set aside. Gently punch down the dough, then turn out to a clean work surface and allow to rest for 5 minutes.
Divide the dough in half and keep the half you are not working with covered with plastic wrap.
On a well-floured surface, roll the dough into a 16-inch square. Crumble half of the filling over the surface of the dough, reserving 2 tablespoons of the filling, and leaving a ½-inch border around the edges of the dough.
Brush the egg wash around the border of the dough. Starting at one side, roll the dough up tightly into a log, pinching the ends together to seal. Holding one end of the dough in each hand, twist the dough lengthwise five or six times.
Brush the top of the log with the egg wash, then carefully sprinkle the remaining 2 tablespoons of filling over the top of the log, pressing it into the egg wash. If any falls off the sides, pick it up and press it into the top.
Fold the dough in half into a horseshoe shape, then cross the right half over the left half. Pinch the ends together to seal and form a figure eight. Holding one end of the dough in each hand, twist the dough two more times, then nestle it into the prepared loaf pan.
Repeat steps #9 through #12 with the second half of dough.
Preheat oven to 350 degrees F with rack in lower third of oven.
Make the Streusel Topping
In a medium bowl, whisk together the powdered sugar and flour. Using a pastry blender or fork, cut in the butter until the mixture resembles coarse crumbs with larger chunks throughout.
Brush the top of each loaf with the egg wash and sprinkle each loaf evenly with half of the streusel topping. Cover the loaves loosely with plastic wrap and place in a warm, draft-free spot until the dough has expanded and puffed a bit, about 30 minutes.
Bake the Babkas
Bake the loaves, rotating halfway through, until a light golden brown, about 55 minutes. Reduce the oven temperature to 325 degrees F and continue baking until deep golden brown and a digital instant-read thermometer inserted into the center of the loaves registers 190 degrees F, about 15 to 30 more minutes. Transfer the pans to wire racks to cool completely. The loaves should be wrapped tightly in plastic wrap and can be stored at room temperature for up to 4 days.
Freezing Instructions - Unbaked: The babka can be frozen in the pan for up to 1 month before baking. Wrap tightly in plastic wrap, and then in foil. When ready to bake, remove from freezer; let stand at room temperature for about five hours before baking as directed.
Freezing Instructions - Baked: Once baked and completely cooled, the babka can be wrapped in plastic wrap, then foil, and placed in a zipper freezer bag for up to 3 months. Thaw in the refrigerator or at room temperature before serving. You could also slice the loaf and freeze the slices individually.
Milk: I use whole milk because I like the higher fat content for baking recipes, but you can get away with 2% here, as well.
Yeast: Instant yeast is sometimes also referred to as bread machine yeast or rapid rise yeast. If you use active dry yeast, please be aware that your rise times will be longer.
Thermometer: If you want to use a thermometer to check the temperature of the milk or the finished bread (which is not necessary, but incredibly helpful), I swear by my Thermapen MK4 instant-read digital thermometer.
Chocolate: I recommend using baking bars that you chop finely for this recipe, as opposed to chocolate chips, which will hold their shape and not melt down as much as chopped chocolate. I like Ghiradelli and Guittard brands. You can substitute bittersweet chocolate if you'd like, but I would not use milk chocolate, as it would be too sweet here.
Cinnamon: It might be strange to see this much cinnamon mixed in with chocolate, but it is not pronounced and it totally elevates the flavor of the filling. I highly recommend leaving it in!
To Make By Hand: If you don't have a stand mixer, you can still make babka! Mix the dough together as directed, using a wooden spoon, then knead by hand on a floured surface until the dough is smooth and slightly tackly, then proceed with the rest of the recipe.
The Original Recipe: If you are interested in the original recipe that yielded 3 loaves, you can find those measurements here.