Feed starter at night before bed. This way when you wake up in the morning, it will be nice and bubbly.
In the morning, combine all ingredients in a mixer and knead until smooth and glossy. The dough will be very wet, but after 10-15 minutes in the stand mixer (or by hand), it will come together.
Cover with plastic wrap, a damp towel, or tight lid and place in a warm spot for 6-8 hours (or until doubled).
Refrigerate for a few hours (or overnight) so that dough is nice and stiff for shaping.
In a pot, add the cocoa powder, sugar, and softened butter. Heat on low until melted, stirring occasionally.
Divide the dough into two equal portions. I really like to use my bench scraper to do this.
Roll out each portion to a 10” by 14” rectangle
Add the filling to the edge, except on one short end, leave about an inch of dough showing. Sprinkle the semisweet chocolate over the filling.
Roll up your dough from the opposite short end.
Cut the roll down the middle and twist.
Add your babka to a loaf pan, cover, and allow to rise until doubled, about 4 hours.
Preheat oven to 350 degrees.
Create an egg wash by beating an egg with water. Brush over the loaf.
Bake 40-45 minutes