In a medium bowl, combine the diced tomato, finely chopped red onion, spinach, crumbled feta cheese, shredded mozzarella cheese, and dried oregano. Toss gently until the ingredients are evenly distributed. I like to squeeze the spinach gently with my hands first to remove any excess moisture—this prevents the quesadillas from becoming soggy during cooking.
Lay out all three flour tortillas on a clean work surface. Divide the Mediterranean filling mixture from Step 1 evenly among the three tortillas, placing approximately 1/3 of the filling on one half of each tortilla. Fold each tortilla in half over the filling, pressing gently to keep everything in place. For even cooking, I press down lightly on the folded quesadillas with my hand to ensure the filling is distributed from edge to edge—this helps them cook more uniformly.
Heat a large skillet or griddle over medium heat and lightly oil the surface (about 1 tablespoon of oil total). Once the pan is hot, carefully place the folded quesadillas in the skillet. Cook for 3-4 minutes on the first side until golden brown and crispy, then flip carefully and cook the second side for another 3-4 minutes until the cheese is fully melted and the tortilla is golden. Work in batches if needed to avoid overcrowding the pan.
Transfer the cooked quesadillas to a cutting board and let them rest for 1 minute. This brief rest allows the cheese to set slightly, making them easier to slice cleanly. Cut each quesadilla in half or into triangular pieces and serve immediately while warm.