01 - Combine diced chicken, olive oil, minced garlic, lemon juice, oregano, thyme, sea salt, and black pepper in a mixing bowl. Toss until evenly coated. Cover and refrigerate for at least 15 minutes, allowing flavors to penetrate the meat.
02 - Heat a large skillet over medium-high heat for 2 minutes. Add marinated chicken in a single layer. Cook for 5-6 minutes, stirring occasionally, until chicken is browned on the outside and cooked through to an internal temperature of 165°F. Transfer to a plate and set aside.
03 - Wipe skillet clean with paper towels. Place one tortilla flat on a clean surface. Sprinkle half of the tortilla with 1/4 cup mozzarella, 2 tablespoons feta, one-fourth of cooked chicken, 2 tablespoons red onion, 2 tablespoons roasted peppers, 2 tablespoons spinach, and 2 tablespoons olives. Fold tortilla in half to create a half-moon shape.
04 - Brush skillet with 1 teaspoon olive oil and heat over medium heat. Place filled quesadilla in pan. Cook for 2-3 minutes until bottom is golden brown and cheese begins to melt. Carefully flip and cook second side for 2-3 minutes until golden and crispy. Transfer to cutting board.
05 - Repeat cooking process with remaining tortillas and filling. Let quesadillas rest for 1 minute before slicing into 4 wedges each. Serve immediately while cheese is still melted and tortillas remain crispy.