01 - Preheat oven to 350°F. Season the chicken breasts evenly with salt and black pepper.
02 - Heat olive oil in an oven-proof skillet over medium heat. Sear the chicken on both sides for 3 to 4 minutes, developing a golden-brown surface.
03 - Transfer the skillet to the oven and bake the chicken for 12 to 15 minutes, or until the internal temperature reaches 165°F. Remove chicken to a plate and cover to keep warm.
04 - In a saucepan over medium heat, melt unsalted butter. Whisk in the flour and cook for 1 minute, stirring continuously.
05 - Gradually pour in milk, whisking constantly until the mixture is smooth and slightly thickened, about 2 to 3 minutes.
06 - Reduce the heat to low. Add cheddar cheese, Parmesan, garlic powder, and Dijon mustard. Whisk until the cheese is fully melted and the sauce is creamy. Adjust seasoning with salt and pepper if needed.
07 - Arrange chicken breasts on serving plates and generously spoon cheese sauce over each. Serve immediately.