01 - In a stand mixer bowl, combine the flour, sugar, and yeast. Add the lukewarm milk, eggs, vanilla extract, and salt. Mix on low speed until a shaggy dough forms. Gradually add the softened butter with the mixer running on low. Increase speed to medium and knead for 8–10 minutes until the dough is smooth, elastic, and pulls away cleanly from the bowl sides. Transfer to a greased bowl, cover with plastic wrap, and let rise in a warm spot until doubled in size, about 1.5 hours.
02 - Place the chopped dark chocolate and butter in a heatproof bowl set over a pot of simmering water (or microwave in 30-second intervals). Stir until completely melted and smooth. Whisk in the powdered sugar, cocoa powder, and orange zest until well combined. Let the filling cool slightly so it thickens to a spreadable consistency.
03 - Punch down the risen dough to release air. On a lightly floured surface, roll the dough into a 16×12-inch rectangle. Spread the chocolate filling evenly over the surface, leaving a ½-inch border along the edges. Starting from one 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 exposed. Carefully transfer the twisted loaf into a greased 9×5-inch loaf pan.
04 - Cover the loaf pan loosely with a damp towel or plastic wrap. Allow the shaped babka to rise in a warm, draft-free area for 45–60 minutes until puffy and nearly doubled.
05 - Preheat the oven to 350°F (175°C). Place the babka on the center rack and bake for 40–45 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 loosely 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 smooth and pourable. Adjust consistency with additional juice or sugar as needed.
07 - Let the 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. Allow to cool completely before slicing. For extra shine and flavor, brush with an additional layer of glaze once fully cooled.