In a medium bowl, combine the diced tomato, red onion, squeezed spinach, crumbled feta, shredded mozzarella, and dried oregano. Toss gently until evenly mixed. Do not overmix or the tomato will release too much juice.

Lay all three tortillas flat on a clean surface. Scoop roughly one third of the filling onto one half of each tortilla, keeping it about half an inch from the edge. Fold the empty half over the filling and press down lightly.

Heat a large skillet over medium heat. Add about 1 teaspoon of olive oil and let it warm for 30 seconds. Slide one folded quesadilla into the pan and cook for 3 to 4 minutes without pressing down until the bottom is deep golden and crispy.

Flip carefully with a wide spatula and cook the second side for another 3 to 4 minutes until the cheese is fully melted and the tortilla is evenly browned. If the cheese is not fully melted, lower the heat slightly and give it one more minute. Cook remaining quesadillas one at a time.

Transfer to a cutting board and rest for 1 full minute before slicing. Cut into halves or triangles and serve immediately while warm.