01 - Preheat oven to 350°F (180°C). Generously season chicken breasts with salt and pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear chicken breasts on each side for 3 to 4 minutes, until lightly browned.
03 - Transfer skillet to the oven and bake chicken for 12 to 15 minutes, or until fully cooked through and internal temperature reaches 165°F (74°C). Remove chicken to a plate and cover to keep warm.
04 - Melt butter in a saucepan over medium heat. Add flour and whisk constantly for 1 minute until bubbly.
05 - Gradually pour in milk, whisking continuously. 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. Whisk until all cheese has melted and the sauce is silky. Adjust salt and pepper to taste.
07 - Arrange chicken breasts on plates and generously spoon warm cheese sauce over them. Serve immediately.