01 - Preheat oven to 350°F. Pat chicken breasts dry and season evenly with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear the chicken breasts on both sides for 3 to 4 minutes until golden brown.
03 - Transfer skillet to the oven and bake the chicken for 12 to 15 minutes or until an internal temperature of 165°F is reached. Remove the chicken from the oven and set aside, covered to keep warm.
04 - In a saucepan over medium heat, melt unsalted butter. Add the flour and whisk constantly for 1 minute to form a roux.
05 - Slowly pour in whole milk, whisking continuously, and cook for 2 to 3 minutes until the mixture is smooth and slightly thickened.
06 - Reduce heat to low. Add shredded cheddar, Parmesan, garlic powder, and Dijon mustard. Continue whisking until all cheese is melted and the sauce is velvety. Adjust salt and pepper to taste.
07 - Place baked chicken breasts on serving plates. Generously spoon warm cheese sauce over the top and serve at once.