01 - Preheat oven to 350°F (180°C). Season chicken breasts evenly with salt and black pepper.
02 - In a large oven-proof skillet, heat olive oil over medium heat. Sear chicken breasts for 3 to 4 minutes per side until well browned.
03 - Transfer the skillet with chicken to the oven. Bake for 12 to 15 minutes, or until the internal temperature reaches 165°F (74°C). Remove chicken, place on a plate, and cover to keep warm.
04 - In a medium saucepan, melt unsalted butter over medium heat. Add flour and whisk constantly for 1 minute to form a roux.
05 - Gradually pour in whole milk while whisking until mixture is smooth and slightly thickened, about 2 to 3 minutes.
06 - Lower heat. Stir in shredded cheddar, grated Parmesan, garlic powder, and Dijon mustard. Whisk until cheese is fully melted and sauce is silky. Season with additional salt and pepper to taste.
07 - Arrange chicken breasts onto plates and generously spoon cheese sauce over each. Serve immediately.