Heat the butter and oil in a large, oven-safe skillet over medium-high heat. Place one flour tortilla in the skillet. Spread a few tablespoons pizza sauce on the tortilla, leaving a little room around the edges. Sprinkle half of the provolone and half of the fontina over the sauce. Sprinkle a third of the mozzarella next, followed by 1 tablespoon Parmesan and 1/2 teaspoon oregano.
Top with the second tortilla and press it down gently. Once the underside is perfectly toasted, carefully flip the quesadilla to the other side.
Spread a few more tablespoons pizza sauce on the toasted side of the tortilla, being sure to leave a little bit of the edges exposed so it looks like a pizza. Sprinkle with another third of the mozzarella and the remaining provolone, fontina, Parmesan and oregano.
Arrange the red bell pepper and red onion on top of the cheeses like you would on a pizza. Do the same with the pepperoni slices and the olives. Top with the remaining mozzarella.
Transfer the pan to the broiler and let cook to melt the cheese on top, about 2 minutes. Carefully transfer the pizzadilla to a cutting board using a large spatula or two smaller spatulas.
Warm up the remaining pizza sauce and serve in a bowl for dipping. Cut the pizzadilla into wedges and garnish with the torn basil.