Preheat oven to 400 F. Brush a 9 inch round pan or cast-iron skillet with olive oil, or line a sheet pan with parchment.
Stir together melted butter, garlic, parsley, salt, black pepper, and red pepper flakes in a small bowl.
Divide pizza dough into 12 equal pieces. Flatten each piece into a small round.
Place a mozzarella cube in the center of each round. Pull edges up and pinch to seal tightly, forming a smooth ball.
Arrange dough balls seam side down in the prepared pan with slight space between them.
Brush tops lightly with beaten egg, then brush generously with the garlic butter. Sprinkle with Parmesan.
Bake until puffed and deep golden, about 14 to 16 minutes. If desired, brush with a little more garlic butter right out of the oven.
Cool 5 minutes, then serve warm. Great with marinara for dipping.
Notes
For extra stretch, use low-moisture whole milk mozzarella. Make ahead: assemble and refrigerate up to 4 hours; bake from cold, adding 2 to 3 extra minutes.