Combine mozzarella, feta, chopped spinach, diced tomato, sliced red onion, and black pepper in a bowl and mix thoroughly.
Spread one quarter of the filling onto half of a tortilla then fold it over to enclose the mixture.
Warm a non-stick pan over medium heat and add the olive oil.
Place the folded tortilla in the pan and cook for 3 to 4 minutes until it turns golden and crisp on the underside.
Flip the quesadilla carefully and cook for another 3 to 4 minutes until the other side is also golden and crunchy.
Take the quesadilla off the heat, cut into wedges, and serve while hot.