Melt the butter in a large Dutch oven (or heavy pot) over medium-low heat until foaming. Add the shallot and cook, stirring frequently, until translucent, about 3 minutes. Add the squash scrapings and seeds, and cook, stirring occasionally, until the butter turns saffron color, about 4 minutes.
Add the water and salt to the pot and bring to a boil over high heat. Reduce the heat to medium-low, place the squash cut-side down in a steamer basket, and lower the basket into the pot. Cover and steam until the squash is completely tender, about 30 minutes. Take the pot off the heat, and use tongs to transfer the squash to a rimmed baking sheet. When cool enough to handle, use a large spoon to scrape the flesh from the skin. Reserve the squash flesh in a bowl and discard the skins.
Strain the steaming liquid through a mesh strainer into a second bowl; discard the solids in the strainer. (You should have 2½ to 3 cups of liquid.) Rise and dry the pot.
Puree the squash in batches in a blender or food processor, pulsing and adding enough reserved steaming liquid to obtain a smooth consistency. Transfer the puree to the pot and stir in the remaining steaming liquid, cream, and brown sugar. Warm the soup over medium-low heat until hot, about 3 minutes. Stir in the nutmeg and adjust the seasonings, adding salt to taste. Serve immediately with an extra drizzle of heavy cream, if desired. Soup can be refrigerated in an airtight container for up to 4 days, or frozen for up to 3 months. Warm over low heat until hot; do not boil.
Notes
If you do not have a pot with a steamer basket, you can make a modification by placing a colander inside the pot and covering it with foil. Alternatively, you can roast the butternut squash in the oven (peel and cut the squash into 1-inch cubes, place on a rimmed baking sheet and roast at 400 degrees for 25 to 30 minutes, until the squash is tender).
To make a vegan version of this soup, substitute coconut milk or almond milk for the heavy cream and coconut oil for the unsalted butter.
You can freeze this soup. To do so, allow it to cool to room temperature, then transfer to a freezer-safe container and store in the freezer for up to 3 months.