Heat the olive oil in a large, deep skillet or Dutch oven over medium-high heat. Add the chicken pieces and cook until browned on all sides, about 5 minutes. Remove the chicken and set it aside.
Add the chopped onion to the skillet and cook until softened, about 3 minutes. Add the minced garlic and cook for 1 minute more until fragrant.
Stir in the diced tomatoes and green chilies, black beans, chopped green chilies, chili powder, cumin, and oregano. Cook for 1 minute, stirring constantly.
Pour in the chicken broth and bring the mixture to a boil. Stir in the rotini pasta. Reduce the heat to medium-low, cover the skillet, and simmer for 10 minutes, stirring occasionally to prevent sticking.
Stir in the heavy cream and return the cooked chicken to the skillet. Continue to simmer uncovered for another 5 to 7 minutes, or until the pasta is tender and the sauce has thickened.
Remove the skillet from the heat. Stir in the Monterey Jack cheese and cheddar cheese until fully melted and the sauce is creamy.
Serve immediately with your choice of toppings.
Notes
If the sauce becomes too thick while simmering, add a splash more chicken broth or water to reach your desired consistency.
You can substitute ground beef for the chicken; brown the beef first and drain any excess fat before proceeding with the onions.
For a spicier dish, use hot Rotel or add 1/4 teaspoon of cayenne pepper with the other spices.