01 - Preheat the oven to 350°F. Season the chicken breasts evenly with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear chicken breasts for 3 to 4 minutes on each side until golden brown.
03 - Transfer the skillet to the oven. Bake for 12 to 15 minutes, or until the internal temperature reaches 165°F. Remove the chicken and keep warm, tented with foil.
04 - In a saucepan over medium heat, melt the butter. Add flour and whisk constantly for 1 minute until smooth.
05 - Slowly add the milk while whisking to avoid lumps. Continue whisking until the mixture is thickened and smooth, about 2 to 3 minutes.
06 - Lower the heat. Stir in cheddar cheese, Parmesan, garlic powder, and Dijon mustard. Whisk until the cheeses are fully melted and the sauce is silky. Season to taste with salt and black pepper.
07 - Arrange the cooked chicken breasts on plates. Generously spoon the cheese sauce over each piece. Serve immediately.