Choose fresh, briny oysters that are small or medium in size.
Preheat oven to 450 degrees with rack in top position. Brush a 9-by-13-inch baking dish with butter. Melt 2 tablespoons butter in a large saute pan over medium heat. Add breadcrumbs and 1/4 teaspoon salt, and cook, stirring frequently, until breadcrumbs are golden brown and crisp, about 10 minutes. Stir in parsley, and remove from heat. Sprinkle half the breadcrumbs evenly in baking dish, and transfer remaining breadcrumbs to a plate.
Wipe pan clean, and return to stove. Melt remaining 4 tablespoons butter over medium-high heat. Saute celery and scallions, stirring occasionally, until scallions just begin to soften but celery is still bright green, about 2 minutes. Stir in thyme. Add sherry, and simmer 30 seconds. Add cream, and bring to a boil. Stir in reserved oyster liquor, the nutmeg, and 1/4 teaspoon pepper. Remove from heat, and stir in oysters.
Spread oyster mixture evenly over breadcrumbs in baking dish. Top with remaining breadcrumbs, and bake until bubbling and oysters are just cooked through, 7 to 8 minutes. Serve immediately.