In a mixing bowl, combine the shredded sharp cheddar cheese, softened cream cheese, diced pimentos, sliced green onions, crumbled bacon, garlic powder, and cayenne pepper. Mix until well combined and creamy. Set aside.
Preheat your oven to 375°F (190°C). Take the boneless, skinless chicken breasts and gently butterfly each breast, creating a pocket for the stuffing. Be careful not to cut all the way through.
Generously fill each chicken breast pocket with the prepared pimento cheese mixture. Use toothpicks to secure the opening if necessary, ensuring the filling stays intact during cooking.
In a shallow bowl, beat the large egg. In another bowl, place the dry breadcrumbs. Carefully dip each stuffed chicken breast into the egg, allowing any excess to drip off, then coat with breadcrumbs. Make sure the chicken is well-covered.
In a skillet, heat the butter and vegetable oil over medium heat. Once hot, add the breaded chicken breasts, cooking for about 3-4 minutes on each side until golden brown.
Transfer the seared chicken breasts to a baking dish and place them in the preheated oven. Bake for 20-25 minutes, or until the internal temperature reaches 165°F (74°C).
Once cooked, let the chicken rest for a few minutes before serving. This will help retain the juices. Serve with your favorite sides, and enjoy the delicious combination of flavors!