01 - Preheat oven to 350°F (180°C). Season chicken breasts evenly with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear each chicken breast for 3 to 4 minutes per side until well-browned.
03 - Transfer the skillet to the oven and bake chicken for 12 to 15 minutes, or until the internal temperature reaches 165°F (74°C). Remove from oven, transfer chicken to a plate, and cover to keep warm.
04 - Melt butter in a saucepan over medium heat. Add flour and whisk continuously for 1 minute to form a roux.
05 - Slowly pour in milk, whisking constantly until the mixture is smooth and begins to thicken, about 2 to 3 minutes.
06 - Reduce heat to low. Whisk in cheddar cheese, Parmesan, garlic powder, and Dijon mustard until cheese melts and sauce is silky. Season with salt and pepper as desired.
07 - Spoon the hot cheese sauce generously over the cooked chicken breasts and serve immediately.