1. Warm oil in a medium skillet over medium-high heat. Add onion and cook, stirring, until softened, about 3 minutes. Stir in spinach and cook, stirring, until heated through, 2 to 3 minutes longer. Transfer to a bowl and stir in cheese and olives.
2. Spread 1/4 of cheese mixture over 1/2 of each tortilla. Fold to cover; press lightly to seal.
3. Place a large skillet over medium-high heat. Cook quesadillas one at a time in skillet, turning once, until golden on both sides and cheese is melted, about 6 minutes total for each. Serve immediately.
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