01 - Preheat oven to 350°F. Season chicken breasts thoroughly with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear chicken on both sides for 3–4 minutes until golden brown.
03 - Transfer skillet to the oven. Bake chicken for 12–15 minutes, or until internal temperature reaches 165°F. Remove chicken and cover to keep warm.
04 - Melt butter in a saucepan over medium heat. Add flour and whisk for 1 minute until blended.
05 - Gradually add milk while whisking constantly. Cook for 2–3 minutes until sauce thickens slightly and becomes smooth.
06 - Reduce heat to low. Stir in shredded cheddar, Parmesan, garlic powder, and Dijon mustard. Whisk until cheese melts and sauce is silky. Adjust seasoning with salt and pepper as needed.
07 - Spoon warm cheese sauce over chicken breasts and serve immediately.