01 - Preheat oven to 350°F. Pat chicken breasts dry and season evenly with salt and ground black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Add chicken breasts and sear each side for 3 to 4 minutes until lightly browned.
03 - Transfer the skillet to the oven and bake for 12 to 15 minutes, or until the chicken reaches an internal temperature of 165°F. Remove chicken, place on a plate, and cover to keep warm.
04 - Melt butter in a saucepan over medium heat. Add flour and whisk for 1 minute to form a roux.
05 - Slowly add milk, whisking continuously to eliminate lumps. Cook for 2 to 3 minutes until slightly thickened.
06 - Reduce heat to low. Stir in shredded cheddar, Parmesan, garlic powder, and Dijon mustard. Whisk until cheese has melted and sauce is smooth. Season with additional salt and black pepper as needed.
07 - Arrange baked chicken breasts on serving plates and pour warm cheese sauce over each portion. Serve immediately.