In a mixing bowl, combine the mozzarella cheese, feta cheese, chopped spinach, diced tomato, thinly sliced red onion, and black pepper. Mix everything together until the vegetables are evenly coated with cheese.

Lay one tortilla flat on your work surface and place one-fourth of the filling mixture on half of the tortilla, spreading it evenly but leaving about half an inch from the edge. Fold the empty half over the filling and press down gently to seal.

Heat a non-stick skillet over medium heat and add about 3/4 teaspoon of olive oil, swirling to coat the bottom of the pan. Wait until the oil shimmers slightly before adding the quesadilla, about 1 minute.

Place the folded quesadilla in the skillet and cook for 3 to 4 minutes until the bottom develops golden brown spots and crispy edges.

Using a wide spatula, carefully flip the quesadilla and cook for another 3 to 4 minutes until both sides are golden and crispy. The cheese should be fully melted. Press down gently with the spatula during the last minute.

Remove from heat and let rest for about 30 seconds, then slice into 3 to 4 wedges using a sharp knife or pizza cutter. Repeat with the remaining three tortillas, adding another 3/4 teaspoon of oil between each one.