In a medium bowl, combine the diced tomato, finely chopped red onion, spinach, crumbled feta, shredded mozzarella, and dried oregano. Toss gently until evenly distributed. Squeeze the spinach firmly with your hands before adding it to remove excess water and prevent soggy quesadillas.

Lay all three flour tortillas flat on a clean work surface. Divide the filling evenly across one half of each tortilla, keeping it about half an inch from the edge. Fold each tortilla closed and press down lightly with your hand to distribute the filling evenly inside.

Heat a large skillet over medium heat and add the olive oil. Let the pan get fully hot before adding the quesadillas. Place one or two at a time without crowding. Cook 3 to 4 minutes on the first side until deep golden brown, flip carefully, and cook another 3 to 4 minutes until the second side is golden and the cheese is fully melted. Do not press down with the spatula.

Transfer the cooked quesadillas to a cutting board and let them rest for 1 minute. Cut into halves or triangles and serve immediately while warm.