01 - Preheat oven to 350°F. Season chicken breasts on both sides with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear chicken on each side for 3 to 4 minutes until golden brown.
03 - Transfer the skillet to the oven. Bake the chicken for 12 to 15 minutes or until the internal temperature reaches 165°F. Remove chicken from the skillet and cover to keep warm.
04 - In a saucepan, melt the butter over medium heat. Add flour and cook, whisking constantly, for 1 minute.
05 - Gradually add milk, whisking continuously until smooth and slightly thickened, about 2 to 3 minutes. Reduce heat to low, then add cheddar, Parmesan, garlic powder, and Dijon mustard. Whisk until cheese is fully melted and sauce is silky. Season with salt and black pepper to taste.
06 - Arrange cooked chicken breasts on plates and spoon cheese sauce over the top. Serve immediately.