01 - Preheat oven to 350°F. Season chicken breasts evenly with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Add chicken breasts and sear for 3 to 4 minutes per side until lightly browned.
03 - Transfer skillet with chicken to the oven. Bake for 12 to 15 minutes, or until internal temperature reaches 165°F. Remove chicken from oven and set aside, covering to keep warm.
04 - In a separate saucepan, melt the butter over medium heat. Add flour and whisk continuously for 1 minute to form a smooth roux.
05 - Gradually pour in whole milk while whisking. Continue to whisk until smooth and slightly thickened, about 2 to 3 minutes.
06 - Reduce heat to low. Stir in cheddar cheese, Parmesan, garlic powder, and Dijon mustard. Whisk until all cheese is melted and sauce is silky. Adjust seasoning with salt and pepper as needed.
07 - Transfer cooked chicken breasts to serving plates. Spoon hot cheese sauce over each piece and serve immediately.