In the bowl of a stand mixer fitted with a dough hook or paddle attachment, add the yeast and the sugar.
Pour the warm milk over the yeast mixture and whisk gently to combine.
Loosely cover the bowl with a clean kitchen towel and allow it to sit until it becomes frothy, about 5-10 minutes.
Add 3 tablespoons of the melted butter, the egg, the salt, 1 teaspoon of the garlic powder, 1 teaspoon of the Italian seasoning, and 1 cup of the bread flour to the yeast mixture and beat on low speed to combine the ingredients, about 1 minute.
Add the remaining flour to the dough mixture and beat on low speed until the dough is soft, about 2 minutes. If the dough feels too sticky, add another tablespoon of the flour.
Transfer the dough to a lightly floured work surface and using lightly floured hands, knead it for 3 minutes. If the dough is too sticky to handle, add 1-3 tablespoons of the flour, but ensure the dough remains soft.
Shape the kneaded dough into a ball.
Place the dough in a greased bowl, cover with plastic wrap, and place in a slightly warm environment to rise until it has doubled in size, about 1 hour-1 hour 30 minutes.
While the dough rises, grease a 9-inch square pan.
In a bowl, mix 1 1/2 cups of the mozzarella and 1/2 cup of the pepperoni.
Punch the risen dough down to release the air.
Pinch off a piece of the dough that is about 1 1/2 tablespoons in size. Then, use your hands to form it into a ball and make an indentation in the center.
Pinch a scant tablespoon of the pepperoni mixture with your fingers and stuff it into the middle of the dough piece.
Press the dough around the pepperoni mixture to seal the filling inside, then place it into the prepared pan.
Repeat this process, starting by pinching a piece of dough and ending with placing it in the prepared pan, until the pan has been filled. There should be about 20-24 balls.
Cover the pan with plastic wrap and allow the balls to rise in a slightly warm environment until puffy, about 30-45 minutes.
In a small bowl, mix the remaining mozzarella and the remaining pepperoni together.
In a skillet over medium heat, add the sausage and the green peppers and cook, stirring and crumbling the meat into bite-size pieces, until the sausage is no longer pink, about 6-7 minutes.
Transfer the meat mixture to a paper-towel-lined plate to drain.
Combine the sausage mixture with the olives.
Adjust the oven rack to the lower third position.
Preheat the oven to 350 degrees F.
Bake the balls for 20 minutes.
Transfer the balls from the oven and sprinkle them with the mozzarella mixture and the sausage mixture.
Loosely tent the pan with foil and bake until lightly browned on top, about 12-15 minutes.
Transfer from the oven and allow the balls to cool.
While the balls are cooling, stir the remaining melted butter, the remaining Italian seasoning, and the remaining garlic powder together.
Brush the garlic butter over the warm rolls.
Serve the pizza balls with a side of the pizza sauce and sprinkle with the basil and the red pepper flakes.