Combine the shredded chicken, chopped green chiles, cumin, garlic powder, and a pinch of salt and pepper in a mixing bowl. Mix until evenly coated.
Lay one tortilla flat and sprinkle a layer of shredded cheese over half of it. Add a layer of the chicken and green chile mixture on top of the cheese, then sprinkle another thin layer of cheese. Fold the tortilla in half to form a semicircle. Repeat with the remaining tortillas.
Heat a skillet or griddle over medium heat and add a small amount of oil or butter. Place a folded quesadilla in the skillet and cook for 2-3 minutes on each side or until the tortilla is golden and crispy and the cheese has melted. Remove from the skillet and repeat with the other quesadillas.
Cut the cooked quesadillas into wedges and serve warm with your favorite toppings, such as sour cream, salsa, or fresh cilantro. Recipe excerpted from Route 66 Recipes: A Culinary Cruise Along the Mother Road , reprinted with permission from Arcadia Publishing.
