01 - In a stand mixer bowl, combine the flour, sugar, and yeast. Pour in the lukewarm milk, eggs, vanilla extract, and salt. Mix on low speed until a shaggy dough comes together.
02 - With the mixer running on low, add the softened butter one tablespoon at a time. Knead for 8–10 minutes until the dough is smooth, elastic, and pulls away cleanly from the bowl.
03 - Transfer the dough to a lightly greased bowl, cover with plastic wrap or a damp towel, and let rise in a warm spot until doubled in size, about 1½ hours.
04 - Melt the chopped chocolate and butter together in a heatproof bowl set over simmering water or in the microwave in 20-second bursts, stirring until smooth. Whisk in the powdered sugar, cocoa powder, and orange zest. Let cool slightly until thickened and spreadable.
05 - Punch down the risen dough. On a lightly floured surface, roll it out to a 16×12-inch rectangle. Spread the chocolate filling evenly, leaving a ½-inch border along the edges. Starting from the long side, roll the dough tightly into a log.
06 - Using a sharp knife, slice the log lengthwise down the center to create two halves. Twist the two strands together, keeping the cut sides facing up. Transfer the twisted loaf into a greased 9×5-inch loaf pan.
07 - Cover the pan loosely and let the shaped babka rise for 45–60 minutes until puffy and nearly doubled.
08 - Preheat the oven to 350°F (175°C). Bake the babka for 40–45 minutes until the top is golden brown and a skewer inserted into the center comes out clean.
09 - Whisk together the powdered sugar, orange juice, and orange zest until smooth. Let the babka cool in the pan for 10 minutes, then turn out onto a wire rack. Drizzle the orange glaze generously over the warm babka.