Preheat the oven to 300 degrees. Spray a large heavy skillet with nonstick cooking spray, add the oil, and heat it over medium heat.
Sauté the chicken and onions until the chicken is no longer pink, about 5 minutes.
Add the spices and cook it for 1 - 2 more minutes. Remove the chicken mixture from the heat.
Heat a large skillet (clean the one you were using or use a new one) over medium heat and spray it with nonstick cooking spray (or use a nonstick skillet).
Place a tortilla in the pan and cover half of it with a handful of cheese, topped with a layer of chicken and arugula or spinach (optional). Fold the tortilla in half, and repeat with a second tortilla, so that each quesadilla’s curved edge is pointed toward the outside of the skillet.
Cook them on each side until they are golden brown, 3 – 4 minutes per side. Carefully transfer the cooked quesadillas to a baking sheet in the preheated oven so they stay warm until all the quesadillas are cooked. Slice each quesadilla in half or in wedges and serve with salsa.