01 - Preheat the oven to 350°F. Season the chicken breasts on both sides with salt and black pepper.
02 - Heat olive oil in a large oven-proof skillet over medium heat. Sear the seasoned chicken for 3-4 minutes per side until lightly browned.
03 - Transfer the skillet with the chicken to the oven and bake for 12-15 minutes, or until the internal temperature reaches 165°F. Remove the chicken from the oven, tent with foil or cover, and reserve on a plate to keep warm.
04 - Melt unsalted butter in a saucepan over medium heat. Add flour and whisk constantly for 1 minute to form a smooth roux.
05 - Gradually add milk while whisking continuously. Cook for 2-3 minutes until smooth and just thickened.
06 - Reduce heat to low. Mix in shredded cheddar, grated Parmesan, garlic powder, and Dijon mustard. Whisk until the cheese fully melts, creating a glossy sauce. Season with additional salt and black pepper as needed.
07 - Arrange the warm, cooked chicken breasts on serving plates. Generously ladle the cheese sauce over each portion and serve without delay.