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 excess liquid if needed and set aside to cool slightly.

Lay out the flour tortillas and sprinkle mozzarella cheese evenly over one half of each tortilla, leaving a half-inch border.

Divide the spinach and onion mixture evenly among the tortillas, spreading it over the mozzarella. Top with crumbled feta cheese. Fold each tortilla in half to create a half-moon shape 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, cook one or two quesadillas in the skillet for 3-4 minutes per side until golden brown and cheese is melted.

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