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 comes together.
02 - With the mixer running on low speed, add the softened unsalted butter one tablespoon at a time, allowing each portion to fully incorporate before adding the next. Continue kneading for 8 to 10 minutes until the dough is smooth, elastic, and slightly tacky.
03 - Transfer the dough to a lightly greased large bowl, turning once to coat. Cover tightly with plastic wrap and set in a warm, draft-free spot until doubled in size, approximately 1½ hours.
04 - While the dough rises, combine the chopped dark chocolate and unsalted butter in a heatproof bowl set over a pot of barely simmering water. Stir occasionally until completely melted and smooth. Whisk in the powdered sugar, unsweetened cocoa powder, and orange zest. Let the mixture cool slightly until it thickens to a spreadable consistency.
05 - Gently punch down the risen dough to release excess gas. On a lightly floured surface, roll it out to a 16×12-inch rectangle. Spread the chocolate filling evenly across the surface, leaving a ½-inch border along all edges.
06 - Starting from one 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 outward, keeping the layers visible. Carefully transfer the twisted loaf into a greased 9×5-inch loaf pan.
07 - Cover the pan loosely with a clean kitchen towel and let the shaped babka rise until puffy and nearly doubled, about 45 to 60 minutes.
08 - Preheat the oven to 350°F (175°C). Bake the babka on the center rack for 40 to 45 minutes, rotating halfway through, until the top is deeply golden and a skewer inserted into the center comes out clean.
09 - While the babka bakes, whisk together the powdered sugar, fresh orange juice, and orange zest in a small bowl until completely smooth and pourable. Adjust consistency with additional juice if needed.
10 - Let the babka rest in the pan for 10 minutes, then turn it out onto a wire cooling rack. While still warm, drizzle the orange glaze generously over the top, allowing it to drip down the sides. For extra shine and deeper flavor, brush on a second coat of glaze once the babka has cooled completely.