Warm 1 tablespoon of olive oil in a skillet over medium heat. Add the chicken, garlic, and oregano, cooking for about a minute to heat through and blend the flavors.
Heat the remaining olive oil in a large skillet set over medium heat.
Lay two tortillas in the skillet.
Sprinkle each tortilla with a portion of mozzarella, followed by the warmed chicken mixture, spinach, feta, and tomato. Add another layer of mozzarella on top.
Place a second tortilla over each filled one to form two quesadillas.
Cook for 4 to 5 minutes per side, or until both sides are crisp and golden and the cheese has fully melted. Slice and serve warm.