For the Candied Walnuts:
For the Cardamom Cream:
Preheat oven to 350ºF.
Season squash with salt, pepper, and a dash of nutmeg. Drizzle squash with olive oil and place 1/2 tablespoon butter in cavity. Place squash in a baking pan filled with about 1/4 inch water. Cover pan tightly with foil and roast squash for 40 to 50 minutes, until tender when pierced with a knife.
When squash is cool enough to handle, scoop out the flesh and place in a food processor. Put the remaining butter in a saucepan over medium-high heat and cook until the butter is slightly browned, one to two minutes. Add the onions, cinnamon, clove, peppercorns, and star anise. Cook, stirring occasionally, for six to seven minutes, until the onions are tender. Add the brown sugar, chicken stock, and cream and simmer for 20 minutes. Purée in a blender and strain through a chinoise. Season with salt and pepper.
Divide soup between two bowls. Spoon a dollop of cardamom cream on each and garnish each with two candied walnuts. Finish with drops of pumpkin seed oil.
For the Candied Walnuts:
Bring a saucepan of salted water to a boil and drop in the walnuts. Boil them until tender, about five minutes. Remove heat and drain. Place powdered sugar in a small mixing bowl. Add nuts and toss to coat. Leave nuts in the powdered sugar for 20 minutes. Heat the peanut oil in a small heavy-bottomed saucepan to 365°F. Fry the walnuts in two batches. Constantly stir them in the oil until the walnuts are a light golden brown, about two minutes. (They will continue to brown when removed from the oil, so be careful to not over-brown in the oil.) Remove from oil and toss them with sea salt to taste. This recipe makes extra walnuts, which will keep up to one week in a tightly closed container.
For the Cardamom Cream:
Place all of the ingredients in a small mixing bowl and whisk until soft peaks are formed.