Melt half the butter in a Dutch oven over medium heat. Add the shallot and cook until softened, about 3 minutes. Stir in the reserved squash seeds and fibers and cook until the butter turns a deep orange and smells nutty, about 4 minutes.

Stir in the water and salt and bring to a boil. Reduce the heat to a simmer, place the squash halves cut-side down in a steamer basket, and lower the basket into the pot. Cover and steam until the squash is completely tender and a paring knife easily pierces the neck, 30 to 40 minutes.

Transfer the cooked squash to a rimmed baking sheet using tongs. Once cool enough to handle, scrape the cooked squash flesh from the skin using a large spoon and discard the skins.

Strain the cooking liquid through a fine-mesh strainer into a large measuring cup and discard the solids. Working in batches, puree the cooked squash with the strained cooking liquid in a blender until perfectly smooth, about 2 minutes.

Return the pureed soup to a clean pot and stir in the cream, sugar, nutmeg, and remaining butter. Return to a brief simmer, adding more cooking liquid if needed to reach your preferred consistency. Season with salt and pepper to taste and serve hot.