In a microwave-safe bowl, combine vinegar, 1/3 cup water, and dried tomatoes.
Heat, covered, in a microwave oven at full power until steaming, about 45 seconds.
Let stand, stirring occasionally, until tomatoes are soft, about 20 minutes.
Meanwhile, in a 5- to 6-quart pan over high heat, bring about 3 quarts water to a boil.
Add the penne pasta and cook until it's barely tender to bite, 10 to 12 minutes and drain.
As pasta cooks, lay prosciutto strips on a microwave-safe plate and heat in a microwave oven at full power (100%), stirring once, just until hot, 15 to 20 seconds.
Also, pour canned tomatoes into a strainer over a large bowl, then chop the tomatoes and add to juices in bowl.
Add dried tomatoes and soaking liquid, garlic, parsley, pasta, and olive oil.
Mix, and add prosciutto, olive oil, and 1/4-cup cheese.
Mix again, and add salt, pepper, and more cheese to taste.