In a large mixing bowl, combine the flour, instant yeast, sugar, and salt. Add the warm milk, egg, and olive oil. Mix until a soft dough forms, adding a little warm water if needed.
- Knead the dough.Transfer the dough to a lightly floured surface and knead for 8–10 minutes until smooth and elastic. Place it in a greased bowl, cover, and let it rise in a warm place for about 1 hour, or until doubled in size.
- Prepare the filling.In a small bowl, combine the shredded mozzarella, garlic powder, Italian seasoning, and Parmesan cheese, if using.
- Shape the bread.Once the dough has risen, gently punch it down and divide it into 8 equal portions. Flatten each portion into a small circle, place a generous spoonful of the cheese mixture in the center, and carefully seal the edges. Roll each piece into a smooth ball with the seam facing down.
- Arrange and proof.Place the dough balls in a greased baking dish, leaving a little space between them. Cover and let them rise for another 20–30 minutes until slightly puffy.
- Bake until golden.Preheat the oven to 375°F (190°C). Bake for 20–25 minutes, or until the bread is golden brown and cooked through.
- Add the garlic butter.Mix the melted butter with the minced garlic and chopped parsley. Brush the mixture over the hot bread as soon as it comes out of the oven. Sprinkle with Parmesan cheese for extra flavor, if desired.
- Serve warm.Let the bread cool for 5 minutes before serving. Pull apart the soft rolls to reveal the delicious melted mozzarella inside.