In a large skillet, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until softened.
Add the chopped spinach to the skillet and cook for an additional 2-3 minutes until wilted. Remove from heat and stir in the garlic powder, black pepper, and crumbled feta cheese.
Lay a tortilla flat on a clean surface. Sprinkle 1/4 of the mozzarella cheese on one half of the tortilla. Spoon 1/4 of the spinach and feta mixture over the cheese, then fold the tortilla in half.
Heat a non-stick skillet over medium heat and lightly coat with cooking spray or a drizzle of olive oil. Place the folded quesadilla in the skillet and cook for about 3-4 minutes on each side, or until golden brown and the cheese is melted.
Repeat steps 3 and 4 for the remaining tortillas and filling.
Cut each quesadilla into wedges and serve warm.