Sauté the star anise, ginger, onion, and a generous pinch of salt in the butter and oil in a large heavy pan over medium heat. Cook, stirring occasionally, until the onion is soft, about 10 minutes.
Add the paprika and a pinch of cayenne if you wish. Add the squash cubes and fry them for about 8 minutes, stirring. Pour in the stock. Stir and season the soup with salt and black pepper. Bring to a boil over high heat. When the soup boils, lower the heat and let the soup simmer. Partially cover the pan with a lid. Let the soup simmer for 30 minutes, or until the squash is tender.
Remove the star anise (save it for garnish).
Puree the soup with a hand blender for a long time, at least 7 minutes, until very smooth. This really matters—the longer you do it, the smoother the soup!
This soup can easily be made 2 days in advance: Let it cool to room temperature, then cover and keep it in the fridge.
Toss the ginger with the crayfish tails and let them stand for 30 minutes. Sprinkle with some salt and pepper.
Heat a drop of oil in a nonstick skillet over medium heat and fry the crayfish tails for 2 minutes on each side, stirring continuously.
In the meantime, bring the soup to a boil and divide it among six or eight serving bowls.
Make a swirl with some whipped crème fraîche and place 3 or 4 crayfish tails in each bowl. Drizzle some pumpkin seed oil over it and sprinkle with some pepper. You can garnish with the star anise if you saved them.
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