Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Whisk egg, barbeque sauce, Worcestershire sauce, cayenne pepper, garlic powder, and black pepper together in a large bowl; add ground beef and mix well. Mix bread crumbs and minced onion into the ground beef mixture. Scoop sour cream into the beef mixture by the spoonful; continue mixing and adding sour cream just until moist. Form mixture into 6 large patties.
Cook the patties until they are very firm, hot, and grey in the center, 6 to 8 minutes per side. An instant-read thermometer inserted into the center should read 160 degrees F (70 degrees C).
