Make the dough: Place the yeast and sugar in the bowl of a stand mixer fitted with a dough hook or paddle attachment. Or, if you do not own a stand mixer, use a large mixing bowl. Heat the milk on the stove or in the microwave until warm to touch, about 110°F (43°C). Pour warm milk on top of yeast/sugar. Whisk gently to combine, then loosely cover with a clean kitchen towel and allow to sit for 5-10 minutes. The mixture will become frothy.
If you do not have a mixer, you can mix the dough together with a wooden spoon or rubber spatula in this step. Add the melted butter, egg, salt, garlic powder, and Italian seasoning and about 1 cup of the bread flour. Beat on low speed for 1 minute to combine ingredients, then add the remaining flour and beat on low speed for 2 minutes. Dough will be soft. If it feels too sticky, add another tablespoon of flour. Transfer it to a lightly floured work surface. Using lightly floured hands, knead it for 3 minutes. If the dough is too sticky to handle, add 1-3 more tablespoons of flour, but you want a very soft dough. Shape dough into a ball.
Place the dough in a greased bowl (I use nonstick spray to grease) and cover with plastic wrap or aluminum foil. Place in a slightly warm environment to rise until doubled in size, around 60-90 minutes.
As the dough rises, grease a 9-inch square pan, a 9-inch springform pan, or a 10-inch oven-safe cast iron skillet; if using a cast iron skillet that's already seasoned, no need to grease it. A 9-inch round cake pan or pie dish is too small for this recipe. See Notes for other baking pan options.
Prepare the filling: Mix together 1 and 1/2 cups (135g) shredded mozzarella and 1/2 cup (60g) chopped pepperoni in a bowl.
Shape the rolls: When the dough is ready, punch it down to release the air. Pinch off a piece of dough about 1 and 1/2 tablespoons in size (1 ounce/30g). With your hands, form into a ball and make an indent in the center. Pinch a bit of cheese and pepperoni (a scant tablespoon, about 7–8g) with your fingers and stuff into the middle of the dough. Press the dough around it to seal the filling inside, and place the stuffed dough ball into the prepared pan. Repeat with remaining dough and filling until you've filled the pan (you should have about 20–24 balls).
Cover the pan with plastic wrap or aluminum foil and allow to rise once again in a slightly warm environment until puffy, about 30–45 minutes.
Prepare the toppings: In a small bowl, mix together 1/2 cup (45g) mozzarella cheese and 1/4 cup (30g) pepperoni. If you're making the supreme-style option, heat a skillet over medium heat. Add sausage and chopped green pepper. Cook, stirring and breaking up the sausage into bite-size pieces with a wooden spoon or rubber spatula, until sausage is cooked through, about 6–7 minutes. Transfer the mixture to a plate lined with paper towels, to drain. Combine with the sliced olives.
Adjust the oven rack to the lower third position, then preheat oven to 350°F (177°C).
Bake for 20 minutes. After 20 minutes, remove the rolls from the oven and sprinkle on the cheese and pepperoni topping; plus the cooked sausage, peppers, and olives, if making supreme style. Loosely tent with foil, then return to oven and bake for another 12–15 minutes, or until lightly browned on top. For a more accurate test of doneness, the rolls are done when an instant read thermometer reads 195°F (90°C). Remove from the oven and let cool for a few minutes as you prepare the topping.
Make the garlic herb butter: Melt 2 tablespoons of butter and stir in the garlic powder and Italian seasoning. Brush on warm rolls before serving. Serve with a side of pizza sauce, and any other additional pizza toppings such as fresh chopped basil or crushed red pepper flakes.
Cover leftover rolls tightly and store in the refrigerator for up to 5 days.