You can prep this easy appetizer ahead and broil it right before serving. It also works beautifully as a main dish. Serve over orzo tossed with butter, lemon juice, grated parmesan or pecorino cheese and minced flat-leaf parsley.
Peel and clean the shrimp, leaving tails on if you like. (Tails make a nice presentation and a useful handle, but you can serve the appetizer with cocktail forks or toothpicks instead.)
Cut each slice of prosciutto into two or three long strips. Wrap one strip around each shrimp. Place shrimp on a rimmed baking sheet lined with a piece of parchment paper that just fits.
Melt butter in a small pot. Brush about half of the butter over the shrimp. Preheat broiler to high.
While broiler preheats, add garlic and sage to remaining butter. Cook on medium heat for a minute or two, until very fragrant.
Broil shrimp for about 90 seconds, until shrimp are turning opaque and prosciutto begins to cook. Flip shrimp with tongs and broil about 60 seconds more, until just cooked through.
Transfer shrimp to a serving platter. Brush with garlic sage butter and sprinkle with black pepper. Serve immediately.