Combine the lime juice, ají panca paste, garlic, salt, black pepper, cumin and 2 tablespoons (30 ml) of the olive oil in a glass container with a lid.
If not already cleaned, trim the heart of fat, connective tissue and blood vessels. Cut the meat into equal-size chunks, 1 to 2 inches (2.5 to 5-cm) across and 0.5 inch (1.3-cm) thick.
Place the heart chunks in the marinade and toss to combine. Cover and refrigerate for a minimum of hour, up to overnight.
Before grilling, have 6 to 8 skewers ready. If using wooden or bamboo skewers, soak them in water for at least 30 minutes.
Meanwhile, prepare the grill for direct cooking over medium heat (325-375 F / 170 C). Depending on type of grill, this may take 15 to 20 minutes.
Thread the heart pieces onto the skewers. Make sure each piece is spread as flat as possible and leave a very small space between each piece.
Once the grill is hot, brush the cooking grates clean, if necessary (to prevent sticking). Grill the skewers over direct medium heat for 2 to 3 minutes per side for medium rare or to 5 minutes for medium well done. Brush the kebabs with the remaining olive oil at least once during cooking. Do not overcook or else the beef heart will become tough and rubbery.
Serve immediately as an appetizer or with your favourite sides for a meal. This pairs very well with plantain tostones.