In a 10- to 12-inch frying pan over high heat, frequently stir oil, onion, garlic, and prosciutto until onion is lightly browned, 5 to 8 minutes; keep warm.
Meanwhile, in a 4- to 5-quart covered pan, bring 3 quarts water to a boil over high heat.
Add beans and cook, uncovered, until tender-crisp when pierced, 6 to 12 minutes, depending on variety.