In a large bowl, combine ground beef, chorizo, salt, and black pepper; mix well. Shape mixture into eight 1/2-inch-thick patties.
For a charcoal grill, grill patties on the rack of an uncovered grill directly over medium coals for 10 to 13 minutes or until done (160 degrees F), turning once halfway through grilling. (For a gas grill, preheat grill. Reduce heat to medium. Place patties on grill rack over heat. Cover; grill as above.)
Meanwhile, in a small bowl, combine mayonnaise and hot pimenton. Generously spread the top half of each roll with the mayonnaise mixture. Place the burger on the bottom half of the roll and heap with shoestring potatoes. Add roll tops and press together. Makes 8 servings