Preheat oven to 400 degrees. Place pumpkin halves, cut sides down, on a rimmed baking sheet. Bake until soft, about 50 minutes. Scoop out flesh, and puree in a food processor (you should have 2 cups).
Melt 1 tablespoon butter in a small saucepan over medium-high heat. Add reserved seeds and fibers from pumpkin, and cook for 4 minutes. Add stock, water, and thyme, and bring to a gentle simmer. Cook for 9 to 10 minutes.
Meanwhile, melt remaining 5 tablespoons butter in a large saucepan over medium-high heat. Add pumpkin puree, parsnip, potato, and turnip, and cook for 5 minutes. Add shallots, and cook until soft, about 4 minutes. Add wine, and cook until liquid has reduced by half.
Strain pumpkin-seed mixture, reserving broth and discarding solids. Add broth to pumpkin-wine mixture. Bring to a simmer; cook 20 minutes. Let cool.
Pass soup through a food mill into a clean saucepan, or puree in a food processor in small batches until smooth. (If soup does not reach desired consistency using a food processor, press it through a fine sieve to remove any remaining lumps.) Heat soup in a saucepan over medium-high heat. Stir in cream, sugar, salt, and pepper, and serve.