Prepare the Dough
In a large bowl, combine warm milk, sugar, and yeast. Let sit until foamy.
Add eggs and softened butter, then gradually mix in flour and salt.
Knead until smooth and elastic (8–10 minutes by hand or in a stand mixer).
Cover and let rise 1–1.5 hours, until doubled in size.
Make the Chocolate Filling
Melt chocolate and butter together until smooth.
Stir in cocoa powder and powdered sugar. Cool slightly for spreading.
Roll and Shape the Babka
Roll dough into a 10x14-inch rectangle. Spread chocolate filling evenly, leaving a small border.
Roll tightly into a log. Slice lengthwise down the middle.
Twist the two strands together, cut sides facing up.
Transfer to a greased loaf pan, cover, and let rise 45 minutes.
Bake
Preheat oven to 350°F (175°C).
Bake 30–35 minutes until golden brown and cooked through.
Optional: Brush with simple syrup for a glossy finish. Let cool before slicing.