Heat olive oil in a skillet over medium heat. Add red onion and cook for 1–2 minutes until slightly softened.
Add chopped spinach and sauté for 1–2 minutes until wilted. Season with salt and pepper. Remove from heat.
Lay tortillas flat. On half of each tortilla, layer sautéed spinach mixture, feta, and mozzarella cheese.
Fold each tortilla in half to cover the filling.
Spray a clean skillet with nonstick spray or a small amount of olive oil. Cook each quesadilla over medium heat for 2–3 minutes per side, or until golden and cheese is melted.
Slice into wedges and serve warm.