Heat a large skillet over medium heat and add a drizzle of olive oil. Sear the boneless skinless chicken breasts for about 6-8 minutes per side, ensuring they are golden brown and cooked through.

Remove the chicken from the skillet, covering it loosely with foil to keep warm while preparing the cheese sauce.

In the same skillet, reduce the heat to low and add butter until melted. Sprinkle in gluten-free flour to form a roux, stirring constantly for about 1-2 minutes until bubbly and golden.

Gradually whisk in 1 cup of milk, ensuring a smooth consistency, and let it gently simmer for about 3-4 minutes until slightly thickened.

Slowly fold in shredded Monterey Jack cheese into the milk mixture, stirring continually until melted and creamy. Add paprika, cayenne pepper, and salt and pepper to taste.

Slice the cooked chicken into strips and place them back in the skillet with the melted cheese sauce, gently stirring to coat every piece. Serve immediately.