01 - In a stand mixer bowl, combine the all-purpose flour, granulated sugar, and instant dry yeast. Add the lukewarm whole milk, room-temperature eggs, vanilla extract, and salt. Mix on low speed until a shaggy dough forms. With the mixer running on low, gradually add the softened unsalted butter one tablespoon at a time. Increase speed to medium and knead for 8 to 10 minutes until the dough is smooth, elastic, and pulls away cleanly from the bowl. Transfer to a greased bowl, cover with plastic wrap, and let 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 simmering water, or microwave in 30-second intervals, stirring between each until completely smooth. Whisk in the powdered sugar, unsweetened cocoa powder, and orange zest until well combined. Allow the mixture to cool slightly until it thickens to a spreadable consistency.
03 - Punch down the risen dough to release air bubbles. On a lightly floured surface, roll the dough out into a 16 by 12-inch rectangle. Spread the chocolate filling evenly across the surface, leaving a ½-inch border along the edges. Starting from the long side, roll the dough tightly into a log, pinching the seam to seal. Using a sharp knife, slice the log lengthwise down the center to create two halves. Twist the two halves together with the cut sides facing up, keeping the layers exposed. Carefully transfer the twisted dough into a greased 9 by 5-inch loaf pan.
04 - Cover the loaf pan loosely with a damp towel or plastic wrap. Allow the shaped babka to rise for 45 to 60 minutes in a warm, draft-free area until visibly puffy and nearly doubled.
05 - Preheat the oven to 350°F. Bake the babka on the center rack for 40 to 45 minutes until the top is deep golden brown and a toothpick inserted into the center comes out clean. If the top browns too quickly, tent with aluminum foil during the final 10 minutes.
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 consistency with additional juice or sugar as needed.
07 - Let the baked babka cool in the pan for 10 minutes, then turn out onto a wire rack. While still warm, drizzle the orange glaze generously over the top, allowing it to drip down the sides. For extra shine and citrus intensity, brush with an additional layer of glaze once fully cooled.