In a small bowl, mix chili powder, cumin, smoked paprika, garlic powder, onion powder, salt, pepper, and cayenne.
Pat chicken dry, rub with olive oil and seasoning mix.
Heat a large skillet over medium-high heat. Sear chicken for 4–5 minutes per side until golden and cooked through (internal temp 165°F). Remove and set aside.
In the same skillet, melt butter. Stir in flour to make a roux, cooking 1 minute.
Gradually whisk in chicken broth and heavy cream until smooth. Simmer 3–4 minutes until slightly thickened.
Stir in shredded cheese and diced green chilies until melted into a smooth cheese sauce.
Slice or leave chicken whole. Pour cheese sauce over chicken and garnish with cilantro.
Serve with rice, warm tortillas, or roasted vegetables. Add lime wedges for brightness.