01 - Preheat oven to 350°F. Pat chicken breasts dry and season evenly with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear chicken on both sides for 3 to 4 minutes, or until golden brown.
03 - Transfer skillet to the preheated oven. Bake chicken for 12 to 15 minutes, or until fully cooked and the internal temperature reaches 165°F. Remove chicken from skillet, cover, and set aside to keep warm.
04 - In a medium saucepan, melt unsalted butter over medium heat. Add flour and whisk for 1 minute until combined and bubbling.
05 - Gradually pour in whole milk, whisking constantly. Continue to whisk for 2 to 3 minutes until mixture is completely smooth and slightly thickened.
06 - Reduce heat to low. Stir in shredded cheddar cheese, grated Parmesan, garlic powder, and Dijon mustard. Whisk until cheese is fully melted and sauce is silky. Season with salt and black pepper to taste.
07 - Arrange chicken breasts on serving plates and ladle cheese sauce over each piece. Serve immediately.