Season and cook the chicken: Pat chicken breasts dry, mix seasonings in a bowl, rub seasoning blend evenly over chicken. Heat olive oil in large skillet over medium-high heat, cook chicken 5-7 minutes per side until golden brown and cooked through (165°F internal temperature). Remove chicken from skillet and set aside.

Prepare the cheese sauce: In the same skillet, melt butter over medium heat. Whisk in flour and cook for 1 minute until bubbly. Gradually whisk in milk until smooth. Bring to simmer and cook 2-3 minutes until slightly thickened. Reduce heat to low, gradually stir in shredded cheeses until melted and smooth. Add seasonings and diced green chilies (if using), stirring until sauce is creamy and well-combined.

Combine and serve: Return cooked chicken breasts to skillet, spoon cheese sauce over them. Simmer for 2-3 minutes to allow flavors to meld. Serve hot over rice, with tortillas, or alongside fresh salad.