In a stand mixer bowl, combine flour, sugar, yeast, warm whole milk, eggs, orange zest, and vanilla extract. Mix the combination on a low speed with a dough hook until incorporated. Slowly add salt and one tablespoon of butter at a time to the mixture.
Knead mixture for an additional 5–7 minutes until a smooth dough forms.
Transfer the dough to a greased bowl. Seal the bowl with plastic wrap. Let the dough rise at room temperature for 1 hour.
Refrigerate the dough for 2 hours.
Shortly before removing dough from the refrigerator, combine chocolate and butter in microwave-safe bowl, melting in short intervals until smooth. Fold cocoa powder and powdered sugar into chocolate mixture until incorporated.
Once cooled, transfer the chilled dough to a floured surface, shaping it into a 14” by 18” rectangle. Evenly spread the melted chocolate combination over top of the dough.
Roll the dough into a log, starting from the shorter side of the rectangle. Refrigerate the rolled log crease-side down for 10 minutes.
Grease an 8.5"×4.5"×2.5"-inch loaf pan followed by a sheet of parchment paper lining the bottom.
Cut the log lengthwise into two strips with a serrated knife. Arrange the strips cut side up, crossing one strip over the other to form an "X". Twist the remaining ends together into a combined coil. Place the twisted dough in the prepared loaf pan, ensuring the chocolate layers face upward.
Place a pot of boiling water on the oven’s bottom rack (with the oven turned off), then set the babka dough on the middle rack to rise in the humidity for 1 hour.
Remove the babka and the pot of water from the oven. Preheat the oven to 325°F. Bake the babka uncovered for 30 minutes, then cover it loosely with foil, baking for another 30–35 minutes.
As the babka bakes, heat sugar and water in a small pot over medium heat until dissolved, then remove from heat.
Once removed from the oven, generously brush the babka with the hot sugar mixture. Allow the babka to cool in the loaf pan for 20 minutes, then transfer to a wire rack to cool completely. Enjoy!