In a skillet, cook the chorizo over moderate heat, breaking it up with a spoon, until lightly browned, 8 minutes. Scrape into a bowl and let cool, then break into small clumps.

Add 1 tablespoon of water to the skillet and simmer over low heat. Add the butter to the skillet a few cubes at a time, whisking constantly until melted before adding more. Stir in the chorizo and lime juice and season with salt. Keep warm over very low heat.

Light a grill. Place the oysters on the grill, flat side up. Grill over high heat until the shells open slightly. Carefully transfer to a platter and, using kitchen gloves or a mitt, remove the top shell. Spoon the chorizo butter onto the oysters and garnish with a cilantro leaf and lime zest. Serve right away.