Preheat the oven to 350 degrees F.
Place squash and onion in a medium saucepan, and cover with water. Add 1 tablespoon salt, and bring to a boil. Reduce heat, and simmer until tender, about 20 minutes. Drain well, and transfer to a large bowl.
Add 1 cup bread crumbs, eggs, cream, thyme, 1/2 cup cheese, black pepper, cayenne pepper, and remaining teaspoon salt. Gently stir to combine. Pour into a 2-quart shallow baking dish. Spread remaining 1/2 cup cheese and remaining 1/2 cup bread crumbs over top. Cover, and bake until set, about 30 minutes. Uncover, and continue baking until top is browned, about 10 minutes more.
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