Pat the chicken breasts dry, then season on both sides with chili powder, garlic powder, onion powder, cumin, paprika, oregano, salt, and pepper.

Heat the olive oil in a large skillet over medium-high heat and sear the seasoned chicken until golden on both sides and cooked through, then transfer to a plate and tent with foil.

Reduce heat to medium, add butter to the same skillet, and whisk in the flour to form a smooth roux; cook for about 1 minute until lightly golden.

Slowly pour in the milk while whisking constantly to avoid lumps, then add a pinch of salt and the cayenne pepper; simmer gently until the sauce thickens.

Remove the pan from heat and gradually stir in the shredded cheese until completely melted and the sauce is smooth and creamy.

Return the cooked chicken breasts to the skillet, spoon the cheese sauce over the top, and warm briefly over low heat before serving with cilantro and lime wedges.