To prepare oysters: Position an oven rack about 4 inches from the broiler; preheat broiler to high. Spread a layer of rock salt (or a layer of crumpled foil) on a large rimmed baking sheet to keep the oysters level. Shuck oysters, leaving them on the half shell. Nestle the oysters, in their shells, in the salt (or foil). Top each oyster with desired amount of the tomato butter. Broil, watching closely, until the butter is bubbling and the edges of the oysters begin to curl, 5 to 10 minutes, depending on the size of the oysters.