Preheat oven to 425 degrees. Preheat pizza stone for 10 minutes. Stack tortillas 2 high and prebake for 2 minutes. Flip the tortillas and cook another 2 minutes. Remove from oven.
Spread pesto on top of tortillas. Grate about 1/3 cup of fresh mozzarella on top of each pizza, add the tomatoes, red onions, black olives and another 1/3 cup of fresh grated mozzarella. Sprinkle each pizza with dried basil to taste.