1. In a large saucepan over medium-high, combine the olive oil, garlic, onion, paprika, basil and oregano. Sauté until the onion is tender and seasonings are fragrant, about 5 minutes.
2. Add the ground beef and prosciutto. Sauté until the beef is cooked through and the prosciutto begins to brown, about 8 minutes. Add the tomato sauce, ketchup and vinegar and bring to a simmer. Stir in the Parmesan, then season with salt and pepper.
3. Set the oven to broil.
4. Arrange the bottom halves of the rolls on a baking sheet, then spoon some of the sloppy Joe mixture onto each. Top each with a slice of provolone, then broil just until the cheese starts to melt. Top with the other halves of the rolls.
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