Combine first 4 ingredients and, if desired, ground red pepper, garlic powder, and sugar in a bowl. Stir in mayonnaise, and work into a chunky paste. Store in refrigerator until ready to use.
Remove meat and pimento cheese from refrigerator at least 30 minutes before cooking. Heat a cast-iron or other heavy skillet over medium-high heat. Form 4 (1-inch-thick) patties, seasoning with salt and black pepper. Cook patties 4 minutes per side or until medium, flipping only once. Remove grease from pan. Add buns to skillet, and warm until just toasted. Spread pimento cheese onto warm patties or buns, and assemble burgers.