01 - Preheat oven to 350°F. Season chicken breasts with salt and pepper on both sides.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear chicken breasts for 3 to 4 minutes per side, until golden brown.
03 - Transfer skillet to the oven and bake for 12 to 15 minutes, or until chicken reaches an internal temperature of 165°F. Remove chicken from skillet and cover to keep warm.
04 - In a saucepan over medium heat, melt unsalted butter. Add flour and whisk constantly for 1 minute to form a smooth roux.
05 - Gradually pour in whole milk, whisking continuously until mixture is smooth and lightly thickened, about 2 to 3 minutes.
06 - Reduce heat to low. Stir in shredded cheddar, grated Parmesan, garlic powder, and Dijon mustard. Continue whisking until cheese is completely melted and sauce is velvety. Season with salt and pepper as needed.
07 - Place chicken breasts on serving plates. Spoon warm cheese sauce generously over each portion and serve immediately.