Add flour, sugar, and yeast to the bowl of a stand mixer (or large mixing bowl if mixing by hand). Add milk, eggs, zest, and vanilla extract. Mix until dough comes together. With mixer on low, gradually add butter and salt, mixing after each addition until fully incorporated.

Knead the dough for several minutes, scraping the sides of the bowl as needed. If dough is too sticky, add a little more flour. Continue kneading until dough is smooth and pulls away from the sides of the bowl.

Transfer the dough to a greased bowl and cover with plastic wrap. Allow it to rise at room temperature for 1 hour, then transfer to the refrigerator to chill for at least 2 hours, or up to 24 hours.

Melt chocolate and butter in a microwave-safe bowl at 50% power, stirring until smooth. Sift in cocoa powder and powdered sugar, stirring to combine. Set aside to cool.

Grease an 8.5x4.5x2.5 inch loaf pan with butter and line the bottom with parchment paper.

Remove the dough from the refrigerator and roll it out on a floured surface into a 14x18-inch rectangle (short side facing you).

Spread the chocolate filling evenly over the dough. If the filling is too thick, reheat it slightly to make it more spreadable.

Starting from the short end, roll the dough tightly into a log and seal the edge. Refrigerate the log for 5–10 minutes to make slicing easier.

Using a sharp serrated knife, slice the dough lengthwise into two long strips. Place the strips open-side-up and twist them together to form a rope with the chocolate layers facing up.

Boil water in a small pot. Place the pot of hot water at the bottom of your oven to create a warm, humid environment. Place the loaf pan on the middle rack and allow the dough to rise for 1 hour.

Preheat the oven to 325°F (163°C). Once the dough has risen, remove the water from the oven and bake the babka for 30 minutes uncovered. Tent with foil and bake for another 30–35 minutes, or until the loaf reaches 200°F (93°C).

While the babka is baking, prepare the sugar syrup by combining water and sugar in a skillet over medium-low heat. Stir until the sugar dissolves.

Brush the sugar syrup over the hot babka once it’s out of the oven. Use all of the syrup. Let the babka cool in the pan for 20–30 minutes before removing it to a wire rack to cool completely.

Slice the babka with a serrated knife, wiping the knife clean between each slice.