01 - Preheat oven to 350°F. Pat chicken breasts dry and season both sides evenly with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Add chicken breasts and sear for 3 to 4 minutes per side until golden brown.
03 - Transfer the skillet with seared chicken to the oven. Bake for 12 to 15 minutes, or until the internal temperature reaches 165°F. Place cooked chicken on a plate and keep covered to retain warmth.
04 - Melt butter in a medium saucepan over medium heat. Add flour and whisk constantly for 1 minute to form a roux.
05 - Gradually pour in whole milk, whisking continuously to prevent lumps. Cook for 2 to 3 minutes until the sauce thickens slightly.
06 - Reduce heat to low. Stir in shredded cheddar, grated Parmesan, garlic powder, and Dijon mustard. Whisk until cheese is fully melted and sauce becomes smooth. Season with additional salt and pepper as needed.
07 - Arrange chicken breasts on serving plates. Spoon warm cheese sauce over each piece and serve immediately.