01 - Preheat oven to 350°F (180°C). Season chicken breasts evenly with salt and 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 skillet to oven and bake chicken for 12 to 15 minutes, or until the internal temperature reaches 165°F (74°C). Remove from oven and cover chicken to keep warm.
04 - In a medium saucepan over medium heat, melt unsalted butter. Add flour and whisk constantly for 1 minute until smooth.
05 - Gradually whisk in whole milk. Continue whisking for 2 to 3 minutes until sauce thickens slightly and is smooth.
06 - Reduce heat to low. Stir in shredded cheddar cheese, grated Parmesan, garlic powder, and Dijon mustard. Whisk until cheese melts completely and the sauce is velvety. Season with salt and pepper.
07 - Arrange baked chicken breasts on serving plates. Spoon the hot cheese sauce over each breast and serve immediately.