In a small bowl, combine the warm milk, sugar, and yeast. Let it sit for about 5-10 minutes until it becomes frothy.

In a large mixing bowl, whisk together the flour and salt.

Add the activated yeast mixture, melted butter, eggs, and vanilla extract to the flour mixture. Mix until a dough forms.

Transfer the dough to a floured surface and knead for about 5-7 minutes until smooth and elastic.

Place the dough in a greased bowl, cover it, and let it rise in a warm place for about 1 hour, or until doubled in size.

In a medium bowl, combine the chocolate chips, cocoa powder, powdered sugar, softened butter, and vanilla extract. Mix until well combined.

Once the dough has risen, punch it down and roll it out on a floured surface into a rectangle (about 16x24 inches).

Evenly spread the chocolate filling over the dough, leaving a small border around the edges.

Starting from one long side, tightly roll the dough into a log. Pinch the seams to seal.

Cut the log in half lengthwise to expose the filling. Twist the two halves together.

Carefully place the twisted dough into a greased 9x5 inch loaf pan.

Cover the loaf with a kitchen towel and let it rise for another 30-45 minutes.

While the dough rises, preheat your oven to 350°F (175°C).

Brush the top of the babka with the beaten egg.

Bake for 30-40 minutes, or until the top is golden brown.

Allow the babka to cool in the pan for about 10 minutes, then transfer it to a wire rack.

Once cooled, slice and enjoy your delicious Chocolate Babka!