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. 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.
02 - Transfer the dough to a lightly greased large bowl, turning once to coat. Cover tightly with plastic wrap and let rise in a warm, draft-free spot until doubled in size, about 1½ hours.
03 - While the dough rises, combine the chopped dark chocolate and butter in a heatproof bowl set over simmering water (or microwave in 30-second bursts). Stir until completely melted and smooth. Whisk in the powdered sugar, cocoa powder, and orange zest. Let the mixture cool slightly until it thickens to a spreadable consistency.
04 - Punch down the risen dough and turn it out onto a lightly floured surface. Roll into a 16×12-inch rectangle. Spread the chocolate filling evenly over the surface, leaving a ½-inch border along all edges. Starting from one long side, roll the dough tightly into a log, pinching the seam to seal.
05 - Using a sharp knife, slice the log in half lengthwise to create two long strands, cut sides facing up. Twist the two strands together, keeping the exposed chocolate layers facing upward. Carefully transfer the twisted loaf into a greased 9×5-inch loaf pan, tucking the ends under to fit.
06 - Cover the pan loosely with a damp towel or oiled plastic wrap. Let the shaped babka rise until puffy and nearly doubled, 45–60 minutes.
07 - 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. If the top browns too quickly, tent loosely with aluminum foil during the last 10 minutes.
08 - Cool the babka in the pan for 10 minutes, then turn out onto a wire rack. While still warm, whisk together the powdered sugar, orange juice, and orange zest until smooth, then drizzle the glaze generously over the top. Allow the glaze to set before slicing.