01 - In the bowl of a stand mixer, combine the flour, sugar, and yeast. Pour in the lukewarm milk, add the eggs, vanilla extract, and salt. Mix on low speed until a shaggy dough forms. With the mixer still on low, add the softened butter one tablespoon at a time. Increase speed to medium and knead for 8 to 10 minutes until the dough is smooth, elastic, and pulls away cleanly from the bowl. Transfer to a lightly 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 barely simmering water. Stir gently until fully melted and smooth. Remove from heat and whisk in the powdered sugar, cocoa powder, and orange zest. Allow the mixture to cool slightly until it thickens to a spreadable consistency.
03 - Punch down the risen dough and turn it out onto a lightly floured surface. Roll into a 16 by 12 inch rectangle. Spread the chocolate filling evenly over the surface, leaving a ½ inch border along the edges. Starting from the long side, roll the dough tightly into a log, pinching the seam to seal. 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 by 5 inch loaf pan.
04 - Cover the pan loosely with a clean kitchen towel or plastic wrap. Let the shaped babka rise in a warm, draft free area for 45 to 60 minutes until puffy and nearly doubled.
05 - Preheat the oven to 350°F. Bake the babka on the center rack for 40 to 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 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 completely smooth and pourable. Adjust consistency with additional juice or sugar as needed.
07 - Allow the babka to cool in the pan for 10 minutes, then carefully turn it out onto a wire cooling rack. While still warm, drizzle the orange glaze generously over the top, letting it drip down the sides. Let cool completely before slicing.