Preheat oven to 350 degrees F (175 degrees C). Grease a large baking dish with butter.
Place olive oil, sun-dried tomatoes, basil, and olives in a food processor; pulse until finally chopped.
Season scallops with seafood seasoning, salt, and pepper. Fold each slice of prosciutto in half lengthwise. Rub tomato mixture over scallops and wrap each with a slice of prosciutto. Arrange wrapped scallops on the prepared baking dish, seam sides down.
Bake in the preheated oven until prosciutto is crispy and scallops are opaque, about 15 minutes.