Preheat oven to 400°F. Arrange squash halves, cut sides down, in a 13- x 9-inch baking dish. Add 1/4 cup water, and cover with aluminum foil. Bake until squash is tender but still firm, 45 minutes to 1 hour. Set aside until cool enough to handle, about 20 minutes. Reduce oven temperature to375°F.
While squash cools, melt 4 tablespoons of the butter in a large skillet over medium-high until a piece of chopped onion sizzles when added to butter. Add chopped onion, bell pepper, and celery. Cook, stirring occasionally, until mixture is fragrant, about 5 minutes. Add garlic and white parts of scallions. Cook, tossing often, until mixture is softened, about 2minutes. Transfer mixture to a large bowl.
Add 2 tablespoons of the butter to skillet, and melt over medium-high. Once butter bubbles up, add shrimp. Cook, tossing often, until bright pink and firm, about 2 minutes. Add ham, Creole seasoning, salt, and black pepper. Remove from heat, and toss to combine. Add reserved onion mixture to shrimp mixture in skillet, and toss to combine. Transfer to a large bowl, and set aside.
Remove and discard seeds from cooled squash halves.Carefully scoop out flesh from each squash half using a spoon, leaving a1/4-inch shell. Set shells aside. Coarsely chop squash flesh, add to shrimp mixture in large bowl, and stir to combine. Add eggs, green parts of scallions,1 1/2 cups of the breadcrumbs, and 2 tablespoons of the parsley, and stir to combine. (Stuffing should be moist but not wet, with ingredients evenly mixed throughout.)
Arrange squash shells snugly in a 13- x 9-inch baking dish or a rimmed baking sheet, with larger, firmer shells around the edges and any torn or broken shells wedged in place among the sturdy ones. Fill shells evenly with prepared stuffing.
Melt remaining 1 tablespoon butter in a small microwavable bowl on HIGH for 30 seconds. Stir remaining 1/4 cup breadcrumbs and 2 tablespoons parsley into butter. Sprinkle breadcrumb mixture evenly overstuffed squash.
Bake at 375°F until stuffing is firm, fairly dry, and lightly browned, 30 to 40 minutes. Transfer squash to a serving platter, and serve hot or warm.