Pour warm milk into a small bowl. Sprinkle yeast and pinch of sugar over milk; let stand until foamy, about 5 minutes.
In a bowl, whisk together 3/4 cup sugar, 2 eggs, and egg yolks. Add egg mixture to yeast mixture, and whisk to combine.
In the bowl of an electric mixer fitted with the paddle attachment, combine flour and salt. Add egg mixture, and beat on low speed until almost all the flour is incorporated, about 30 seconds. Change to the dough hook. Add 2 sticks butter, and beat until flour mixture and butter are completely incorporated, and a smooth, soft dough that's slightly sticky when squeezed is formed, about 10 minutes.
Turn dough out onto a lightly floured surface, and knead a few turns until smooth. Butter a large bowl. Place dough in bowl, and turn to coat. Cover tightly with plastic wrap. Set aside in a warm place to rise until doubled in bulk, about 1 hour.
Place chocolate, remaining cup sugar, and cinnamon in a large bowl, and stir to combine. Using two knives or a pastry cutter, cut in remaining 1 1/2 sticks butter until well combined; set filling aside.
Generously butter three 9-by-5-by-2 3/4-inch loaf pans; line them with parchment paper. Beat remaining egg with 1 tablespoon cream; set egg wash aside. Punch back the dough, and transfer to a clean surface. Let rest 5 minutes. Cut into 3 equal pieces. Keep 2 pieces covered with plastic wrap while working with the remaining piece. On a generously floured surface, roll dough out into a 16-inch square; it should be 1/8 inch thick.
Brush edges with reserved egg wash. Crumble 1/3 of the reserved chocolate filling evenly over dough, leaving a 1/4-inch border. Refresh egg wash if needed. Roll dough up tightly like a jelly roll. Pinch ends together to seal. Twist 5 or 6 turns. Brush top of roll with egg wash. Carefully crumble 2 tablespoons filling over the left half of the roll, being careful not to let mixture slide off. Fold right half of the roll over onto the coated left half. Fold ends under, and pinch to seal. Twist roll 2 turns, and fit into prepared pan. Repeat with the remaining 2 pieces of dough and remaining filling.
Heat oven to 350 degrees. Brush the top of each loaf with egg wash. Crumble 1/3 of streusel topping over each loaf. Loosely cover each pan with plastic wrap, and let stand in a warm place 20 to 30 minutes.
Bake loaves, rotating halfway through, until golden, about 55 minutes. Lower oven temperature to 325 degrees. Bake until babkas are deep golden, 15 to 20 minutes more. Remove from oven, and transfer to wire racks until cool. Remove from pans; serve.
Babkas freeze well for up to 1 month.