Line a baking sheet with kitchen parchment. Set the beef on it, then use 2 forks to gently break it up and spread over the sheet. In a small bowl, combine the paprika, cumin, salt and pepper, then sprinkle over the beef. Freeze until the meat is very cold and beginning to firm up at the edges, about 20 minutes.

Use a rubber spatula to gently fold the spice mixture into the beef without compacting the beef; it's OK if the spices are not completely blended. Let stand 10 to 15 minutes to allow the beef to soften slightly, then divide it into 4 even portions. Shape each into a 4 -inch patty about ½-inch thick.

Prepare a grill for direct, high-heat cooking. For a charcoal grill, spread a large chimney of hot coals evenly over the grill bed; open the bottom grill vents. For a gas grill, set all burners to high. Heat the grill, covered, for 5 to 10 minutes, then clean and oil the cooking grate.

Grill the burgers until well charred on the first side, about 4 minutes. Using a wide metal spatula, flip the patties and cook until well charred on the second side and the center reach 120°F for rare or 125°F for medium-rare, another 4 to 5 minutes. Transfer to a plate and let rest for 5 minutes. Set each burger on a bun and top with smoked paprika and cumin ketchup.