Combine the butter, olive oil, garlic, and Essence in a medium saucepan over medium heat and cook until the butter is melted and the garlic just begins to sizzle. Remove from the heat and set aside until cooled slightly. Stir in the parsley.

Using an oyster knife, shuck the oysters, leaving the oyster nestled in the side of the shell that is more cup-shaped. Make sure to sever the muscle attaching the oyster to the shell.

Preheat a grill to high.

Working in batches, place the oysters on the grill and spoon about 2 teaspoons of the butter-garlic mixture over each oyster. Top each oyster with a pinch of Parmesan and a pinch of Romano. Close the grill and cook until the butter sizzles and the oysters puff up, 5 to 6 minutes.

Using tongs, remove the oysters from the grill and serve on platters with lots of French bread for dipping.