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. Transfer to a greased bowl, cover with plastic wrap or a damp towel, and let rise in a warm spot until doubled in size, about 1½ hours.
02 - Place the chopped dark chocolate and butter in a heatproof bowl set over a pot of barely simmering water. Stir gently until fully melted and smooth. Remove from heat and whisk in the powdered sugar, cocoa powder, and orange zest until well combined. Let the mixture cool slightly until it thickens to a spreadable consistency.
03 - Punch down the risen dough to release air. On a lightly floured surface, roll the dough out into a 16×12-inch rectangle. Spread the chocolate filling evenly over the dough, leaving a ½-inch border along the edges. Starting from the long side, roll the dough tightly into a log, sealing the seam. 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 9×5-inch loaf pan.
04 - Cover the loaf pan loosely with a damp towel or oiled plastic wrap. Allow the shaped dough to rise in a warm, draft-free area for 45–60 minutes until puffy and nearly doubled.
05 - Preheat the oven to 350°F. Bake the babka on the center rack for 40–45 minutes until the top is deep golden brown and a skewer inserted into the center comes out clean or with only moist crumbs. If the top browns too quickly, tent loosely with aluminum foil during the last 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 baked babka cool in the pan for 10 minutes, then turn 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 flavor, brush on a second coat of glaze once the babka has fully cooled. Slice and serve.