Preheat oven to 350 degrees F. Spray a 9x13-inch baking pan with nonstick cooking spray; set aside.
Melt butter in a large skillet over medium- high heat. Add flour and whisk until combined and cook, stirring continuously, for 1 minute. Slowly whisk in broth until completely smooth. Cook, stirring occasionally, for 5 minutes or until sauce thickens. Remove from heat and mix in Greek yogurt and green chiles; set aside.
Combine cooked chicken and one cup of cheese in a bowl. Divide chicken and cheese evenly between 8 tortillas, roll up and place seam side down in prepared pan. Pour sauce over the top and sprinkle on remaining cheese.
Bake for 20 minutes, or until heated through, then turn oven to high broil and cook for 1-2 more minutes or until golden brown. Top with fresh cilantro before serving.