Adjust an oven rack to the top position and preheat the broiler to high.
Melt the butter in a large skillet over medium heat, then and add the celery, green pepper and onion and cook until soft, 8 to 10 minutes. Add the lump and claw crab meat and heavy cream and stir together. Cook over medium-high heat, stirring constantly, until the mixture has thickened, 6 to 8 minutes.
Stir in the lemon juice, Worcestershire, chili sauce, black pepper, hot sauce, Creole seasoning and cornbread. Turn off the heat and spoon 2 to 3 heaping tablespoons of the crab stuffing into each tartlet pan. Sprinkle the Parmesan over the top of the stuffing and place the tartlet pans on a rimmed baking sheet. Broil until the tops are golden brown, 4 to 5 minutes (watch the stuffing closely as broiler intensities vary). Serve immediately.
Lump crab meat has a sweet flavor and often comes in large chunks while claw meat has a stronger taste and a finer texture. If no claw meat is available, you can substitute an equal amount of lump crab meat. If you don't have 2 3/4-inch tartlet pans you can bake off the stuffing in a baking dish, though it would be more of a side dish than an appetizer; you can also halve the recipe and bake the stuffing in 12 tartlet pans. The stuffing can be turned into crab cakes by placing mounds (3 tablespoon each) on a greased foil-lined baking sheet about 1 inch apart. Sprinkle each with Parmesan and broil on the middle oven rack until browned, 5 to 6 minutes; turn the crab cakes over and brown the other sides for an addition 5 to 6 minutes.