The magic of a babka is the combination of gooey chocolate and soft, pillow dough. We've supersized the typical loaf into an enormous twisted wheel that you can cut into wedges--or simply pull apart if you can't help yourself.
For the dough: Warm the milk in a small saucepan over low heat until a thermometer registers 100 to 110 degrees F. Sprinkle in the yeast and a pinch of granulated sugar. Set aside undisturbed until foamy, about 5 minutes.
Whisk together the flour and remaining granulated sugar in a large bowl.
Combine the butter, vanilla and yolks in the bowl of an electric mixer fitted with a paddle attachment and mix on low until combined. Add the yeast mixture and continue to mix on low until combined. Add the flour mixture and mix on low until a thick and slightly sticky dough forms and comes together, about 1 minute. Switch to the dough hook and knead on medium speed, adding up to 1/4 cup more flour if needed to make a soft, smooth ball that sticks to the hook, 3 to 4 minutes.
Coat 2 large bowls with cooking spray. Cut the dough in half, form each into a ball and add one ball to each bowl, turning to coat in the cooking spray. Cover the bowls with plastic wrap and let rise at room temperature until the dough has doubled in size, about 2 hours.
For the filling: Microwave the chocolate and butter in a medium microwave-safe bowl in 30-second intervals, stirring in between each, until melted and smooth. Fold in the granulated sugar and set aside.
Line a baking sheet with parchment. Punch down one ball of dough and turn it out onto a lightly floured surface. Knead a few times, then roll into a rectangle 12 inches by 16 inches, keeping the longer side closest to you. If the chocolate filling has seized and is no longer spreadable, microwave for 30 seconds. Spread half of the chocolate filling all over the dough, leaving a 1-inch border. Starting from the long side, gently roll up the dough so you have a long log. Position it seam-side down. Using a bench scraper or sharp knife, cut the log in half lengthwise so you have 2 long pieces. Twist each piece 4 times. Form one twisted piece into a tight coil (it should look like the center of a cinnamon roll) and carefully transfer to the prepared baking sheet. Coil the second twisted piece around the first. Repeat the rolling, filling, twisting and coiling process with the remaining dough ball. You should have 1 giant twisted babka roll (it might get messy, but that is part of the fun). Cover the baking sheet with clean kitchen towels and let rest for 30 minutes.
Position an oven rack in the center of the oven and preheat to 350 degrees F.
Beat the whole egg with 1 tablespoon water. Brush the roll all over with the egg wash. Bake until puffed and golden brown, about 40 minutes. Let cool on the baking sheet for 10 minutes, then transfer to a cutting board.
For the glaze: Microwave the cream cheese in a microwave-safe bowl until softened, 10 to 15 seconds. Add the confectioners' sugar and milk and whisk until smooth. Drizzle the glaze on top of the roll and sprinkle with flaky sea salt.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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