Cut base off escarole; rinse and drain leaves. Cut leaves crosswise into 1/4-inch-wide strips.
Set a 4- to 5-quart pan over medium-high heat. When hot, add oil, onion, garlic, and prosciutto; stir often until onion is limp, 3 to 5 minutes.
Add broth and beans, cover, and bring to a boil over high heat. Stir in escarole and cook just until wilted, about 1 minute. Add salt and pepper to taste. Ladle into bowls and offer cheese to add to taste.