Dissolve the yeast in the warm milk. Stir in melted butter, sugar, and egg. Add flour to the bowl and place the salt on top of the flour. Now mix everything well, then knead the dough on a floured surface. Let the dough rise at room temperature for about 1 hour.
Mix the pesto and crushed garlic together.Cut the mozzarella into smaller pieces.
When the dough has risen, divide it into 12 equal pieces. The easiest way is to roll the dough into a long sausage, then halve it until you have 12 pieces. Press each piece flat and place 1 good tsp of pesto and some mozzarella on each.
Fold the dough around the filling all the way and pinch the ends together with your fingertips to get a nice round bun. Place the buns next to each other in a baking dish with the “seam sides” down.
Brush the buns with milk and spread the remaining pesto and mozzarella on top. Sprinkle with salt and parsley.
Let the buns rise again for 30 minutes and then bake them for about 30 minutes at 200 degrees Celsius (392 degrees Fahrenheit) until they are nicely golden - serve warm with your favorite dishes.