To a medium mixing bowl, add the grated cheddar, cream cheese, pimentos, mayonnaise, garlic powder, onion powder, smoked paprika, hot sauce, salt, pepper, and Worcestershire sauce. Use a wooden spoon to mix all of the ingredients together until combined. Refrigerate the pimento cheese while you prepare the burgers.
To a large mixing bowl, add the ground meat, panko breadcrumbs, Worcestershire sauce, seasonings, and egg. Use your hands to massage the ingredients together until everything is evenly mixed into the meat.
Divide the ground meat mixture into 8 evenly sized portions and pat them into uniform patties using your hands. Using a two-tablespoon cookie scoop or a measuring spoon, scoop two tablespoons of pimento cheese onto the palm of your hand and flatten it into a small disc that will fit into the center of the burgers.
Place the pimento cheese disc in the center of a burger patty and place another burger patty on top of the pimento cheese. Gently shape the burgers and seal the edges so that the pimento cheese is fully enclosed.
Repeat this process for the remainder of the burgers until you have 4 stuffed burgers. Place the burgers on a plate or baking sheet lightly coated in olive oil so they do not stick and refrigerate the burgers while you heat your grill or grill pan.
Prepare your grill or grill pan by heating it over medium-high heat and lightly coating the cooking surface with olive oil.
Once the grill or grill pan is hot, place the burgers on the grill and cook for 4-5 minutes per side, or until grill marks appear and the burgers are cooked through. Serve pimento cheese-stuffed burgers on toasted brioche buns with red onion, lettuce, and tomato!