In a bowl combine all ingredients except the oysters and mix thoroughly to combine. Transfer butter mixture to a piece of plastic wrap and roll up to form a tight log and freeze until firm.
Preheat a grill to high.
Place the washed oyster shells on a baking sheet and top each shell with 1 oyster. Remove the butter from the freezer and unwrap. Slice the butter into 24 rounds and place 1 round on top of each oyster. Place the oysters on the preheated grill and cook until the oysters are just cooked through, curled around the edges and the butter is melted and bubbly, 4 to 6 minutes.