Peel and devein the shrimp, leaving the tails on. Mix salt, pepper, pimentón de La Vera and olive oil, add the shrimp and toss to coat.
Wrap each shrimp with a piece of jamón about two inches long, and skewer the shrimp so the ham is held securely around the shrimp. Place the skewers over a high temperature grill and cook for 1 to 2 minutes per side, or until the shrimp are opaque and the jamón is crispy at the edges. Serve immediately.