Scrub the oyster to remove any mud or grit and rinse under cool water, set aside.
In a small saucepan, melt the butter and add the worcestershire sauce, smoked paprika, cayenne pepper, lemon juice and parsley - stir to combine and remove from heat.
Place the oysters flat side up on the hot grill (you don't want the oyster liquor to escape -- so make sure the rounded side is resting on the grill grates). Cook on the grill for 3-4 minutes, just until the oysters crack open slightly. Transfer the oysters to a platter.
Using an oyster shucker, slip the tip of the shucker into the opened crack in the oyster. Run the oyster shucker back to the hinge of the oyster and twist it to open. If the oyster is still attached to the muscle on the shell, run the shucker between the oyster and the muscle to detach, being careful not to spill any of the liquid. Arrange the oysters on a platter and spoon one teaspoon of the butter sauce over each oyster. Garnish with a few drops of your favorite hot sauce (we like Crystal). Serve.