For the babka dough: In the bowl of a stand mixer fitted with the kneading hook, whisk together the milk, sugar, and salt. Mix in the active dry yeast and let rest for 5 minutes. Add the egg and whisk to incorporate. Using a fork, gradually incorporate the flour into the wet ingredients, then start kneading the dough. Gradually incorporate the butter a couple tablespoons at a time into the dough as it is kneading, letting it fully incorporate into the dough before adding more. Once all the butter is incorporated, keep kneading the dough, adding a bit more flour if it is too sticky and keeps crawling up the hook. After about 7 minutes, the dough should be smooth and elastic.
Transfer the dough to a large, oiled mixing bowl and cover with a clean kitchen towel. Let rest in a warm spot for about 1 hour, or until the dough has doubled in size.
For the tahini and chocolate babka filling: Sift the powdered sugar and cocoa powder together. Set aside.
In a small saucepan, melt the chocolate and butter together. Transfer to a mixing bowl, then stir in the tahini, powdered sugar and cocoa. Place the filling in the fridge for 15 minutes to let it thicken slightly. The chocolate and tahini filling should remain at a spreadable consistency.
To assemble the chocolate babka: Transfer the babka dough to a lightly floured working surface. Roll the dough out into a large rectangle, about the size of a baking sheet (13 x 9 in/33 x 23 cm). Spread the chocolate and tahini filling all over the surface of the dough. Roll the dough up from the long side of the rectangle until you get a log. Slice the log in half to create two shorter logs (each about 6 1/2 in/16.5 cm long). Set one log aside.
Using a very sharp knife, cut one log right down the center, lengthwise. Lay both sliced pieces side-by-side, open sides up, then press the tops together and twist them around one another. Transfer to one of the prepared loaf pans. Repeat to prepare the second babka.
Transfer the loaf pans to a warm spot, cover with a clean kitchen towel, and let rest for 1 hour more. Alternatively, you can loosely cover the pans with plastic wrap and refrigerate overnight.
To bake the chocolate babka: Preheat the oven to 350°F (175°C). Using a pastry brush, brush the surface of the babkas with beaten egg, then sprinkle with coarse sugar (if desired) and toasted sesame seeds. Bake the babkas for about 30 minutes (or up to 45 minutes if the babka dough is cold from the fridge), or until the chocolate babkas are puffed and golden brown. Chocolate babka should sound hollow when you lightly tap on it.
Let the babkas cool slightly on a wire rack, then unmold, slice and enjoy warm. Alternatively, you can let the babkas cool completely, unmold, wrap in plastic wrap, and freeze for up to 1 month. To serve, let the babkas thaw in the fridge overnight, then reheat in a 300°F (150°C) oven for 10 minutes.
Note: Leftover babka makes delicious French toast!
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