01 - Preheat the oven to 350°F. Generously season the chicken breasts on both sides with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear the chicken for 3 to 4 minutes per side until golden brown.
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 the chicken from the skillet, place on a plate, and cover to retain warmth.
04 - In a saucepan over medium heat, melt the butter. Add the flour and whisk constantly for 1 minute to form a smooth roux.
05 - Gradually pour in the milk, whisking continuously, until the mixture is smooth and has slightly thickened, about 2 to 3 minutes.
06 - Reduce heat to low. Stir in the shredded cheddar, grated Parmesan, garlic powder, and Dijon mustard. Whisk until cheeses are fully melted and the sauce is velvety. Season with additional salt and pepper if needed.
07 - Ladle the warm cheese sauce over the cooked chicken breasts and present immediately.