Begin by preheating your oven to 375°F (190°C), ensuring it's ready to create that delicious crispy exterior.
Place the flour tortillas on a clean work surface. Take a spoonful of pizza sauce and spread it evenly across each tortilla, making sure to leave a small margin around the edges to prevent spillage during rolling.
In a medium-sized mixing bowl, combine the shredded mozzarella and cheddar cheeses with the sliced bell peppers and mushrooms. Sprinkle in the dried oregano, garlic powder, and season with salt and black pepper. Mix everything together until well combined and coated.
Evenly distribute the cheesy vegetable mixture over the pizza sauce on each tortilla, spreading it out so every bite will be flavorful.
Starting from one end, carefully roll each tortilla tightly into a log shape, ensuring the filling remains tightly packed inside.
Arrange the rolled tortillas seam-side down on a baking sheet lined with parchment paper to prevent sticking. Lightly brush the tops with olive oil for an added golden finish.
Bake in the preheated oven for 15-20 minutes, or until the tortillas are crispy and golden brown, filling your kitchen with an irresistible aroma.
Once baked, remove the rolls from the oven and allow them to cool for a couple of minutes. Then, slice each roll into bite-sized pieces, perfect for sharing (or not!).
Serve the warm pizza rolls on a platter, accompanied by a small bowl of additional pizza sauce for dipping. Garnish with fresh basil leaves for an herbaceous touch.