Heat oven to 350 degrees. Cut brioche into 3/4-inch cubes. Spread on a 17-by-12-inch baking sheet; bake until dry and golden, 10 minutes. Transfer to a wire rack to cool.
Melt butter in a medium skillet over medium heat. When hot, add onion, celery, garlic, salt, and pepper. Cook, stirring occasionally, until onions are softened, 3 minutes. Add nutmeg, cayenne, cognac, and oyster liquor; cook until liquid is absorbed, 1 minute. Add oysters and cream; cook 30 seconds. Remove from heat.
In a large bowl, toss together brioche, oyster mixture, and parsley. Use for stuffing immediately. Note: If baking outside the turkey, spread in a buttered 9-by-13-inch baking pan. Bake until golden on top, about 20 minutes. Stir stuffing, and bake another 20 minutes.