If using an outdoor grill, preheat to medium-high (about 400–450°F). For broiler, set the oven rack 4–6 inches from the heat source and preheat the broiler.

If your oysters aren’t shucked yet, carefully shuck them keeping each oyster in its bottom shell with the natural juice (liquor). Discard top shells.

In a small bowl, combine the softened butter, minced garlic, lemon zest, lemon juice, chopped parsley, and a pinch of salt and pepper. Mix until smooth. Stir in half the Parmesan and the panko breadcrumbs if using.

Spoon about 1 teaspoon (or a small dollop) of the garlic Parmesan butter over each oyster, spreading gently so the topping covers the meat but keeps the liquor.

Arrange oysters on a grill-safe pan or directly on a hot grill grate so they sit flat. If using a broiler, place them on a baking sheet lined with foil.

Grill or broil until the butter is bubbling and the tops are lightly browned, about 3–6 minutes depending on heat intensity. Watch closely—the oysters can go from perfect to overdone quickly.

Remove oysters, sprinkle the remaining Parmesan over the hot tops, add an extra grind of pepper, and serve immediately with lemon wedges.