Preheat the grill and prepare for direct grilling with lump charcoal. Target the temperature in the grill at 500 degrees F.
Layer slightly crumbled aluminum foil onto a sheet pan. Place shucked oysters onto sheet pan and gently press down so the oysters sit well on the pan.
Place one heaping teaspoon of the butter into each oyster.
Place gently over direct heat and grill for 4 - 6 minutes. The butter will bubble and remove when you start to see the edges of the oyster flesh slightly brown. Remove with high heat gloves or tongs. However tongs can be difficult with the edges of oysters causing the liquid to fall out.
Serve warm in the half shell over a plate that has been layered with coarse salt.
For the Compound Butter
Combine all ingredients in small bowl with a fork. Use 1 heaping teaspoon of compound butter per oyster. Reserve some to add more after they come off the grill.