How to Make It
Light a grill. In a food processor, pulse the butter with the tarragon, hot sauce, salt and pepper until blended. Transfer the tarragon butter to a sheet of plastic wrap and roll it into a 2-inch-thick log. Refrigerate the butter until slightly firm, about 15 minutes. Slice the butter into 36 pats.
Place the oysters on the hot grill, flat-side up. Cover the grill and cook until the oysters open, about 5 minutes. Using tongs, transfer the oysters to a platter, trying to keep the liquor inside. Quickly remove the top shells and loosen the oysters from the bottom shells. Top each oyster with a pat of tarragon butter and return the oysters to the grill. Cover the grill and cook until the butter is mostly melted and the oysters are hot, about 1 minute. Serve right away.