In a covered 5- to 6-quart pan over high heat, bring broth, wine, and pasta to a boil, then simmer until pasta is tender to bite, about 20 minutes total.
Meanwhile, in an 8- to 10-inch frying pan over medium-high heat, stir prosciutto with butter until crisp, about 5 minutes. Drain on paper towels.
Stir peas and basil into soup and heat until peas are hot, 1 to 2 minutes.
Ladle into bowls and add prosciutto. Sprinkle with cheese to taste.