Prosciutto Lamb Burgers

Name: Prosciutto Lamb Burgers
Ingredients: 1/2 cup plain dried bread crumbs; 1/4 cup chopped fresh flat-leaf Italian parsley; 1 large egg, lightly beaten; 2 tablespoons whole milk; 1/2 cup grated Pecorino Romano; 1/4 cup chopped sun-dried tomatoes; 3/4 teaspoon salt; 3/4 teaspoon freshly ground black pepper; 1 pound ground lamb; 6 large slices prosciutto, sliced medium-thin (for wrapping the burgers); 1/4 cup olive oil; Fresh basil leaves, for topping each burger; Fresh tomato slices, for topping each burger; Extra-virgin olive oil, for drizzling; Balsamic vinegar, for drizzling