Make the chocolate babka dough

Cup of Yum
1. Pour the warm milk into a small bowl. Sprinkle with the yeast and a pinch of sugar and let stand until foamy, about 5 minutes.
2. In a bowl, whisk together the sugar, 2 of the eggs, and the egg yolks. Add the egg mixture to the yeast mixture and whisk to combine.
3. In the bowl of an electric mixer fitted with the paddle attachment, combine the flour and salt. Add the egg mixture and beat on low speed until almost all the flour is incorporated, about 30 seconds.
4. Change to the dough hook. Add 2 sticks of butter and beat until the butter is completely incorporated and the mixture forms a smooth, soft dough that's slightly sticky when squeezed, about 10 minutes.
5. Turn the dough onto a lightly floured surface and knead a few turns, just until smooth. Butter a large bowl. Place the dough in the bowl and turn to coat. Cover the bowl tightly with plastic wrap and let rest in a warm place until doubled in size, about 1 hour.

Make the filling

1. In a large bowl, combine the chocolate, sugar, and cinnamon and stir to combine. Add the 1 1/2 sticks of butter and, using 2 knives or a pastry cutter, cut in the butter until well combined.

Asemble the chocolate babkas

1. Generously butter three 9-by-5-by-2 3/4-inch loaf pans and line them with parchment paper. Beat the remaining egg with the cream.
2. Gently punch down the dough and transfer it to a clean surface. Let the dough rest for 5 minutes.
3. Cut the dough into 3 equal portions. Keep 2 portions covered with plastic wrap while working with the remaining portion.
4. On a generously floured surface, roll the dough out into a 16-inch square that's 1/8-inch thick. Crumble a scant 1/3 of the chocolate filling evenly over the dough, leaving a 1/4-inch border. Brush the border with the egg wash and, starting at one side, roll the dough up tightly like a jelly roll. Pinch the ends together to seal. Holding an end of the dough in each hand, twist it 5 or 6 turns. Brush the top of the roll with the egg wash and carefully crumble 2 tablespoons of the filling over the left half of the roll, being careful not to let mixture slide off. Fold the right half of the roll over onto the coated left half, then fold the ends of the dough underneath and pinch it to seal. Twist the roll 2 turns and nestle it into the prepared pan.
5. Repeat with the remaining 2 pieces of dough and the remaining filling. Don't discard the egg wash just yet. (The babka loaves can be frozen for up to a month before baking. Remove from the freezer and let stand at room temperature for about 5 hours before baking.)

Make the streusel topping

1. In a large bowl, combine the sugar, flour, and butter. Using a fork, stir until the ingredients are fully combined and the streusel is in pieces ranging in size from crumbs to about 1-inch (25-mm) clumps.
2. Heat the oven to 350°F (176°C).
3. Brush the top of each loaf with the egg wash. Crumble 1/3 of the streusel topping over each loaf. Loosely cover each pan with plastic wrap and let stand in a warm place 20 to 30 minutes.
4. Discard the plastic wrap and bake the loaves, rotating them halfway through, until golden, about 55 minutes. Lower the oven temperature to 325°F (163°C) and bake until the babkas are a deeper shade of golden, 15 to 20 minutes more.
5. Remove from the oven and transfer the pans to wire racks to cool to room temperature. Turn the chocolate babka out from their pans and cut them into thick slices.