01 - Preheat oven to 350°F. Pat chicken breasts dry with paper towels and season both sides 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 and bake for 12 to 15 minutes, or until the internal temperature reaches 165°F. Remove chicken to a plate and cover loosely to keep warm.
04 - Melt butter in a saucepan over medium heat. Add flour and whisk for 1 minute until the mixture is smooth and bubbling.
05 - Slowly add milk, whisking constantly until the sauce is smooth and starts to thicken, about 2 to 3 minutes.
06 - Lower the heat. Stir in cheddar, Parmesan, garlic powder, and Dijon mustard. Continue whisking until the cheese melts and the sauce is silky. Adjust seasoning with salt and black pepper as needed.
07 - Arrange chicken breasts on serving plates and ladle cheese sauce over each portion. Serve immediately.