Whisk together the vinegar and oil and season with salt and pepper in a large bowl.
Cook green beans in a 3 to 4-quart saucepan of boiling salted water 2 minutes, then add shallot and cook until beans are crisp-tender, about 2 minutes more. Drain in a colander and plunge into a large bowl of ice and cold water to stop cooking. Drain well, then add to dressing in bowl along with cannellini beans and toss well.
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