Prepare a grill or grill pan over medium-high heat. Brush the grill with vegetable oil. In a medium bowl, combine the beef, pork, vinegar, paprika, cumin, cayenne, and garlic powder. Season with salt.
Shape beef mixture into 4 equally-sized patties, about 4 inches wide. Using your thumb, press a shallow indent into the center of each burger.
Place buns on grill cut side down and grill until lightly toasted, about 30 seconds. Remove to a plate and keep warm.
Grill patties until crust develops on bottom side, about 5 minutes. Flip and cook 4 minutes more. Top each burger with two slices of cheese, cover the grill, and cook until cheese is melted and meat is no longer pink in center about 2 minutes more. Remove burgers to a plate.
To assemble, spread bottom buns with ketchup. Top with lettuce, shoestring fries, and a patty. Close the sandwich with top bun. Serve immediately.
Recipe by 5* trending recipes with videos at https://food.theffeed.com/2021/07/20/melty-grilled-cheesy-frita-cubana/