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1
Remove stem ends and any strings from beans. In a 6- to 8-quart pan over high heat, bring 2 quarts water to a boil. Add beans and cook until tender-crisp to bite, about 4 minutes. With a slotted spoon, transfer beans to a bowl of ice water to cover. When cool, lift beans out and put in a wide, shallow bowl.
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2
Add onions to boiling water and cook just until tender when pierced, about 4 minutes. With slotted spoon, transfer to ice water.
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3
Meanwhile, scrub potatoes and yams. Put in boiling water, adding more water if needed to cover. Cook until vegetables are tender when pierced, about 25 minutes. Drain.
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4
While potatoes and yams cook, drain onions and peel.
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5
In a bowl, whisk together garlic, mustard, vinegar, and oil.
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6
Peel yams; cut potatoes and yams into 1/2-inch slices.
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7
Place potato and yam slices on a barbecue grill over very hot coals or very high heat on a gas grill (you can hold your hand at grill level only 1 to 2 seconds); close lid on gas grill. Cook, turning once, until grill marks develop on both sides, 2 to 4 minutes total.
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8
Add potatoes, yams, onions, tomatoes, and garlic dressing to beans. Mix gently; season to taste with salt and pepper.
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9
Arrange arugula on a platter, spoon salad onto leaves, and sprinkle with mint.
