Mix milk and water together. Dissolve the yeast in the lukewarm mixture.
Mix in the sugar and the 2 eggs.
Add flour, mix well, and pour the dough out onto a floured surface, where you continue kneading it by hand.
Cut the butter into small cubes and knead it into the dough along with the chopped chocolate. Knead by hand until the butter and chocolate are evenly distributed and the dough is smooth and elastic.
Let the dough rise at room temperature for an hour.
Preheat the oven to 200 degrees Celsius (392 degrees Fahrenheit) (fan-forced).
Divide the dough into 15 pieces, shape them into buns, and place them on a baking sheet lined with parchment paper. Let the buns rise for another 15 minutes.
Beat the remaining egg and brush the buns with it. Bake the buns for 15 minutes in the preheated oven and serve them warm.