01 - Preheat oven to 350°F (180°C). Season the chicken breasts evenly with salt and ground black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear the chicken breasts for 3 to 4 minutes on each side until golden brown.
03 - Transfer the skillet to the oven and bake for 12 to 15 minutes, or until an internal temperature of 165°F (74°C) is reached. Remove the chicken to a plate and cover to keep warm.
04 - Melt unsalted butter in a saucepan over medium heat. Whisk in flour and cook for 1 minute, stirring constantly.
05 - Gradually add whole milk, whisking continuously until the mixture is smooth and begins to thicken, about 2 to 3 minutes.
06 - Reduce the heat to low. Stir in cheddar cheese, Parmesan cheese, garlic powder, and Dijon mustard. Whisk until cheeses are fully melted and the sauce is silky. Season with additional salt and ground black pepper according to taste.
07 - Arrange the baked chicken breasts on plates and generously spoon the cheese sauce over the top. Serve immediately.