Heat oven to 400°F. Brush a 9-inch pan or skillet with olive oil.
Stir together melted butter, minced garlic, 1 tbsp parsley, Italian seasoning, red pepper, salt, and pepper.
Lightly flour your work surface. Roll dough into a roughly 12x15-inch rectangle.
Brush the dough with about half of the garlic-butter mixture.
Scatter mozzarella and half of the Parmesan evenly over the dough.
Roll up tightly from a long side. Pinch the seam to seal and turn seam-side down.
Slice the log into 12 even pieces. Arrange cut-sides up in the prepared pan.
Brush tops with more garlic butter. Sprinkle on the remaining Parmesan.
Bake 16–18 minutes, until puffed and golden at the edges and cheese is bubbly.
Brush with any remaining garlic butter and sprinkle the last 1 tbsp parsley. Rest 5 minutes before serving with warm marinara.