In a medium bowl, stir together shredded mozzarella, crumbled feta, chopped spinach, diced tomato, thinly sliced red onion, and a few grinds of black pepper until evenly mixed. Taste and adjust pepper.

Lay a tortilla flat. Spoon about one fourth of the filling onto one half of the tortilla. Fold the empty half over the filling and press gently to compact. Repeat with the remaining tortillas.

Warm a nonstick skillet over medium heat and add the olive oil, swirling to coat the surface.

Place one filled tortilla in the skillet. Cook until the bottom is golden brown and crisp, about 3 to 4 minutes. Flip carefully and cook the other side for another 3 to 4 minutes until both sides are crisp and the cheese is melted. Adjust the heat slightly if the tortilla browns too fast before the cheese melts.

Remove the cooked quesadilla, let it rest for a minute on a cutting board, then slice into wedges and serve warm.