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1
Heat 2 tablespoons olive oil in a large saucepan over medium heat. Add celery root, onions, celery, leek, and shallots. Cover and cook, stirring occasionally, until soft and translucent, 8 to 10 minutes.
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2
Add stock and bring to a simmer. Place cardamom, cinnamon, coriander, and star anise in a piece of cheesecloth. Using kitchen twine, tie to enclose; add to saucepan. Simmer until celery root is tender, about 35 minutes.
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3
Meanwhile, in a medium skillet, heat remaining teaspoon olive oil. Add brussels sprout leaves and cook, stirring, until lightly browned and just wilted. Remove from heat and set aside.
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4
Add heavy cream to saucepan and return to a simmer; cook 10 minutes more. Meanwhile, heat butter in a small skillet over medium-high heat until melted. Continue heating until butter is golden and fragrant; immediately remove from heat and set aside.
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5
Remove cheesecloth packet from saucepan and discard. Working in batches, transfer mixture to the jar of a blender and carefully blend until pureed. Return puree to a saucepan, add browned butter, and reheat, if necessary. Serve hot, garnishing each bowl with 1 teaspoon reserved brussels sprout leaves, 1 teaspoon chopped apples, 3 tablespoons chestnut puree, and 1 teaspoon croutons.
