Light a grill. In a small bowl, blend the butter with the horseradish, Tabasco, lemon zest, lemon juice and pimentón de la Vera. Season with salt.
Arrange the clams over high heat and grill until they pop open, about 25 seconds. Using tongs, carefully turn the clams over so the meat side is down. Grill for about 20 seconds longer, until the clam juices start simmering. Transfer the clams to a serving bowl. Top each clam with about 1/2 teaspoon of the horseradish-Tabasco sauce and serve with the grilled bread.