In a mixing bowl, combine the mozzarella, feta, chopped spinach, diced tomato, sliced red onion, and a few grinds of black pepper. Stir until the mixture is evenly mixed.

Lay one tortilla flat. Spoon one quarter of the filling onto one half of the tortilla. Fold the empty half over the filling and press gently to seal. Repeat with the remaining tortillas.

Heat a nonstick skillet over medium heat. Add the olive oil and swirl to coat the pan.

Place a filled tortilla in the skillet. Cook until the underside is golden brown, about 3 to 4 minutes.

Flip the quesadilla and cook the other side until golden and the cheeses melt, another 3 to 4 minutes. Adjust heat if necessary.

Transfer the finished quesadilla to a cutting board. Let it rest for 1 minute, then slice into wedges and serve warm.