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Bring a small pot of water to a boil; add 1 tablespoon salt. Blanch fava beans until bright green and tender when pinched, about 2 minutes. Transfer beans with a slotted spoon to a colander and run under cold water to stop the cooking. When cool, peel off the tough outer skins, squeezing the beans from the skins (discard skins).
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Pulse almonds with garlic in a food processor until coarsely ground. Add cheese and the oil; process to a coarse paste. Add mint, and pulse a few times until coarsely chopped. Season with salt and pepper. Transfer to a small bowl, and top with a thin layer to preserve the color.
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Bring a large pot of water to a boil; add 2 tablespoons salt. Cook pasta until al dente according to package instructions (about 4 minutes for dried, 1 minute for fresh); reserve 1/2 cup cooking water, then drain pasta. In a warmed serving bowl, mix pesto with enough reserved cooking water, then drain pasta. In a warmed serving bowl, mix pesto with enough reserved cooking water to form a thin sauce. Add pasta and fava beans, and toss well to combine.
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To serve, divide pasta among four dishes, and top with meatballs; garnish with mint, and sprinkle with more cheese.