Prep. Preheat the oven to 375°F (190°C). Then, grease a 9x13-inch casserole dish with non-stick cooking spray or butter.
Prepare the sauce. Melt the butter in a large Dutch oven (4-quart or larger) over medium heat. Stir in the flour and cook for 2 minutes, stirring constantly to avoid burning. Then, slowly pour the chicken stock, whisking it to combine and prevent lumps. Continue to cook over medium heat until the sauce thickens, stirring frequently.
Add seasonings and cheeses. Stir in the taco seasoning, oregano, garlic, salt, pepper, green chilies, and salsa. Then, heat the mixture until it starts to bubble, stirring occasionally. Next, add the heavy cream, bring it back to a simmer, and reduce the heat to low. Stir in 2 cups of Pepper Jack cheese and 1 cup of Colby Jack cheese. Continue stirring until all the cheese is melted and smooth.
Add pasta and chicken. Remove the sauce from the heat. Stir in the cooked rotini pasta, shredded chicken, and fresh cilantro. Mix well until everything is evenly coated with the sauce.
Bake. Transfer the pasta mixture to the prepared casserole dish. Then, sprinkle the remaining 1 cup of Colby Jack cheese. Bake for 15-20 minutes until the cheese is melted and the edges are bubbling.
Cool. Remove from the oven and allow the casserole to cool for about 5 minutes before serving. You can also top with additional salsa and cilantro for garnish if you want.