01 - Preheat oven to 350°F (180°C). Season chicken breasts 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 until golden brown.
03 - Transfer the skillet to the oven. Bake chicken for 12 to 15 minutes or until thoroughly cooked and the internal temperature reaches 165°F (74°C). Remove chicken to a plate and cover to keep warm.
04 - In a saucepan over medium heat, melt butter. Incorporate flour and whisk for 1 minute until combined.
05 - Gradually whisk in whole milk, stirring constantly to achieve a smooth, slightly thickened mixture, about 2 to 3 minutes.
06 - Reduce heat to low; stir in shredded cheddar, Parmesan, garlic powder, and Dijon mustard. Continue to whisk until the cheese melts and the sauce is silky. Season with salt and additional pepper as desired.
07 - Spoon the hot cheese sauce over cooked chicken breasts. Serve promptly.