In a small bowl, mix together the chili powder, cumin, smoked paprika, garlic powder, cayenne pepper, salt, and black pepper. Rub this seasoning mixture evenly over both sides of the chicken breasts. Heat olive oil in a large skillet over medium-high heat. Add the seasoned chicken and cook for 6-7 minutes per side, until golden brown and cooked through. Remove chicken from skillet and set aside.

In the same skillet, reduce heat to medium and melt the butter. Whisk in the flour and cook for 1 minute until golden. Gradually whisk in the milk until smooth. Cook for 2-3 minutes until the sauce thickens. Reduce heat to low and stir in the shredded cheeses until melted and smooth. Add the diced green chilies and remaining cumin. Season with salt to taste.

Return the cooked chicken to the skillet, spooning the cheese sauce over the top. Simmer for 2-3 minutes to heat through. Serve immediately with your favorite sides like rice, tortillas, or a fresh salad.