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Cook haricots verts in a large pot of boiling salted water until just tender, 3 to 4 minutes. Transfer with a slotted spoon to a bowl of ice and cold water, then drain.
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Add edamame to boiling water and cook 4 minutes. Drain in a colander, then rinse under cold water. If using edamame in pods, shell them and discard pods.
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Cook onion, garlic, bay leaf, rosemary, salt, and pepper in oil in a 2- to 4-quart heavy saucepan over moderately low heat, stirring, until softened, about 3 minutes. Add carrot and celery and cook, stirring, until softened, about 3 minutes.
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Add white beans and stock and simmer, covered, stirring occasionally, 10 minutes. Add haricots verts and edamame and simmer, uncovered, until heated through, 2 to 3 minutes. Add butter, parsley, and chervil (if using) and stir gently until butter is melted. Discard bay leaf and rosemary sprigs.