01 - Preheat oven to 350°F. Season chicken breasts evenly with salt and black pepper.
02 - Warm olive oil in a large oven-proof skillet over medium heat. Sear seasoned chicken breasts for 3 to 4 minutes per side until golden brown.
03 - Transfer the skillet to the oven and bake chicken for 12 to 15 minutes until fully cooked and internal temperature reaches 165°F. Set chicken aside on a plate and cover to keep warm.
04 - Melt butter in a saucepan over medium heat. Add flour and whisk for 1 minute to form a smooth roux.
05 - Gradually whisk in the milk, stirring constantly until the mixture is smooth and begins to thicken, approximately 2 to 3 minutes.
06 - Reduce heat to low. Stir in cheddar cheese, Parmesan, garlic powder, and Dijon mustard. Continue whisking until cheese is fully melted and sauce becomes silky. Adjust seasoning with salt and pepper to taste.
07 - Pour cheese sauce over the warm chicken breasts and serve immediately.