For the dough, mix: warm milk, 1 tablespoon of sugar, and the dry yeast, then let it sit for 10 minutes to activate the yeast.
In another bowl, mix the flour, remaining sugar, and salt.
After the active yeast, add the egg together with the soft butter, combine the ingredients together.
Add the dry ingredients, mix again, and knead for 10-12 minutes. The dough should be soft and sticky to the touch.
Transfer the dough into a buttered bowl, cover it, and let it rise for 90 minutes.
Divide the dough into 9 equal pieces, working with one piece at a time, flattening it into a disc, and filling the center with 2 tablespoons of grated mozzarella.
Enclose the filling with the outer dough and pinch it together to form a ball.
Transfer the dough balls into a butter-greased tray, cover them, and let them rise for 30 minutes.
Bake the buns for 35 minutes at 180 °C, or until they turn golden.
For the butter and garlic topping, mix the melted and cooled butter together with chopped garlic, finely chopped herbs, and salt.
