Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the sliced red onion and cook for 3-4 minutes until softened and translucent.

Add the chopped spinach, dried oregano, salt, and pepper to the skillet. Cook for 2-3 minutes until the spinach has completely wilted. Drain any excess liquid if necessary. Remove from heat and set aside to cool slightly.

Lay out the flour tortillas. Sprinkle mozzarella cheese over one half of each tortilla, leaving a half-inch border from the edge.

Divide the spinach and onion mixture evenly among the tortillas, spreading it over the mozzarella layer. Top with crumbled feta cheese. Use 1/3 to 1/2 cup total filling per quesadilla. Fold the empty half of each tortilla over the filling and press down gently to seal.

Wipe out the skillet and heat the remaining 1 tablespoon of olive oil over medium heat. Once the oil shimmers, place one or two quesadillas in the skillet and cook for 3-4 minutes per side until deep golden brown and cheese is fully melted. Press down gently with a spatula while cooking for even browning.

Remove the cooked quesadillas from the skillet and let them rest for 1-2 minutes before cutting into wedges. Serve immediately.