Preheat oven to 350°F. Grease a 9x13-inch baking dish with cooking spray.
Chicken Filling: In a large skillet over medium heat, add olive oil and diced onion. Saute until onions are softened and lightly browned, about 5 minutes. Add minced garlic to the skillet and sauté for 30 seconds more.
Add cooked chicken, Rotel and taco seasoning to the skillet and stir to combine. Cook until heated through, about 5 minutes.
Turn off heat and add ½ cup of shredded cheese to the chicken mixture and stir until combined. Set aside.
Sour Cream Sauce: In a medium saucepan, melt butter over medium heat. Whisk in flour and cook for 1 minute, stirring constantly.
Slowly pour in chicken broth while whisking until the mixture is smooth and thickened, about 2 minutes.
Stir in cumin, salt, pepper, sour cream and chopped green chilies. Cook the enchilada sauce until heated through, about 2 minutes more. Then add ½ cup of cheese and stir until melted.
Enchilada Assembly: Cover the bottom of the baking dish with about ½ cup of the creamy white sauce. Place a heaping spoonful of the chicken mixture into the center of the tortilla, roll it up and place seam-side down in the prepared baking dish.
Pour sauce over the rolled-up enchiladas and spread it out evenly with a spatula. Top with remaining 1 cup of cheese.
Bake in a preheated oven for 25-30 minutes or until cheese is melted and bubbling.
Let cool for 5 minutes before serving.