01 - Preheat the oven to 350°F. Pat the chicken breasts dry, and season both sides with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear chicken breasts for 3 to 4 minutes on each side until golden brown.
03 - Transfer skillet to the oven and bake for 12 to 15 minutes, or until the internal temperature reaches 165°F. Remove chicken from skillet, set aside, and cover to keep warm.
04 - In a separate saucepan over medium heat, melt the unsalted butter. Add flour and whisk for one minute to form a roux.
05 - Gradually pour in the milk, whisking continuously until smooth and slightly thickened, about 2 to 3 minutes.
06 - Reduce the heat to low. Stir in cheddar cheese, Parmesan, garlic powder, and Dijon mustard. Whisk until the cheese is fully melted and the sauce is silky. Adjust seasoning with salt and pepper.
07 - Spoon the hot cheese sauce generously over the cooked chicken breasts. Serve immediately.