Melt butter in a large pot over medium heat. When it foams, add onion, season with kosher salt and freshly ground black pepper, and cook, stirring occasionally, until onion is softened and translucent, about 5 minutes.
Stir in 2 teaspoons of the ginger and the star anise. Add sweet potatoes and stir to combine.
Add broth and water, and stir well, scraping up any browned bits on the bottom of the pot. Increase heat to high and bring mixture to a boil. Reduce heat to low and simmer, uncovered, until sweet potatoes are completely tender, about 12 minutes. Remove from heat.
Allow soup to cool slightly. Remove star anise pods and discard. Process soup in batches in a blender or food processor until very smooth. Return to the pot and reheat over medium-low heat. Season with additional salt and pepper if necessary. Stir in heavy cream if using.
Combine sour cream and remaining 1/4 teaspoon ginger in a small bowl, stirring until well mixed.
Serve soup in warmed bowls, topped with a dollop of ginger cream.
Beverage pairing: Here’s a big soup with a mouth-filling, creamy texture and lots of exotic spice that cries out for German Riesling. Many Rieslings would be a bit light-bodied for this, so go for one of the biggest you can find, one from the Rheingau. Specifically, hunt down the 2006 Dragonstone Riesling from Leitz, which is medium- to full-bodied and rife with citrus and spice and a good dose of acidity.
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