In a small bowl, combine the warm milk and yeast, letting it sit for 5–10 minutes until frothy.
In a large mixing bowl, whisk together the flour, sugar, and salt.
Add the yeast mixture, eggs, and melted butter to the dry ingredients. Mix well until a dough forms.
Turn the dough onto a floured surface and knead for 8–10 minutes until it’s smooth and elastic.
Place the dough in a greased bowl, cover with plastic wrap, and let it rise for about 1–2 hours, or until doubled in size.
In a medium bowl, mix together the chocolate chips, cocoa powder, sugar, softened butter, and vanilla extract until smooth.
Once the dough has risen, punch it down and turn it out onto a floured surface. Roll it into a rectangle about 1/4 inch thick.
Spread the chocolate filling evenly over the dough, leaving a small border around the edges.
Starting from one long side, roll the dough tightly into a log. Pinch the seams to seal it securely.
Cut the log in half lengthwise to expose the filling. Twist the two halves together, placing the twist into a greased loaf pan.
Cover the loaf pan with plastic wrap and let it rise for another 30–45 minutes.
Preheat your oven to 350°F (175°C) while your dough completes its second rise.
Brush the top of the babka with the beaten egg.
Bake for 30–35 minutes, or until golden brown and a toothpick comes out clean.
Allow the babka to cool in the pan for about 10 minutes, then transfer it to a wire rack.
If desired, dust with powdered sugar before serving.
Slice and enjoy your rich, chocolatey Chocolate Babka!