Heat oven to 425° F. Brush the tortillas on both sides with the oil; prick all over with a fork.
Bake the tortillas on 2 rimmed baking sheets, switching the sheets halfway through, until golden, 5 to 7 minutes per side.
Dividing evenly, top the tortillas with the marinara sauce and mozzarella. Return them to oven and bake until the cheese has melted, 7 to 9 minutes. Sprinkle with the basil.