01 - In the bowl of a stand mixer, combine the all-purpose flour, granulated sugar, and instant dry yeast. Pour in the lukewarm whole milk, add the room-temperature eggs, vanilla extract, and salt. Mix on low speed until a shaggy dough forms. Gradually add the softened unsalted butter, then increase the speed to medium and knead for 8–10 minutes until the dough is smooth and elastic. Transfer the dough to a lightly greased bowl, cover with plastic wrap, and let it rise in a warm spot until doubled in size, approximately 1.5 hours.
02 - Place the chopped dark chocolate and unsalted butter in a heatproof bowl set over a pot of barely simmering water. Stir gently until fully melted and smooth. Remove from the heat and whisk in the powdered sugar, unsweetened cocoa powder, and orange zest until well combined. Allow the filling to cool and thicken slightly before using.
03 - Punch down the risen dough and turn it out onto a lightly floured surface. Roll the dough into a 16x12-inch rectangle. Spread the chocolate filling evenly over the surface, leaving a ½-inch border along the edges. Starting from the long side, roll the dough tightly into a log. Using a sharp knife, slice the log in half lengthwise. Twist the two halves together with the cut sides facing up, keeping the layers visible. Carefully transfer the twisted dough into a greased 9x5-inch loaf pan.
04 - Cover the loaf pan loosely with a kitchen towel or plastic wrap. Let the shaped babka rise in a warm, draft-free area for 45–60 minutes until puffy and nearly doubled.
05 - Preheat the oven to 350°F. Place the loaf pan on the center rack and bake for 40–45 minutes, until the top is deep golden brown and a skewer inserted into the center comes out clean or with only slight moist crumbs.
06 - While the babka bakes, whisk together the powdered sugar, fresh orange juice, and orange zest in a small bowl until completely smooth and free of lumps. Adjust the consistency by adding more juice or sugar as needed.
07 - Let the babka rest in the pan for 10 minutes after removing it from the oven. Turn the loaf out onto a wire cooling rack. While still warm, drizzle the orange glaze generously over the top, allowing it to drip down the sides. Let cool before slicing.