In a medium bowl, stir together the shredded mozzarella, crumbled feta, chopped spinach, diced tomato, thinly sliced red onion, and grind or two of black pepper until evenly mixed. Taste and adjust pepper if needed.

Lay one tortilla flat. Spoon about one fourth of the filling onto one half, keeping it away from the edges. Fold the empty half over the filling and press gently to seal. Repeat for the remaining tortillas.

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

Place a filled tortilla in the hot skillet. Cook until the bottom is golden brown and crisp, about 3 to 4 minutes.

Turn the quesadilla carefully and cook the other side for another 3 to 4 minutes, until both sides are evenly crisp and the cheese inside is melted.

Remove from the skillet and let rest for a minute so the filling sets. Slice each quesadilla into wedges and serve warm.