Preheat the grill to high.

Season the tuna steaks. In a small bowl combine the melon, prosciutto, shallots, mint, 2 teaspoons vinegar, 2 tablespoons of the olive oil  and season with salt and pepper. Allow to sit and let the flavor develop for 15 to 20 minutes.

Place the tuna steaks on the grill and cook for 2 to 3 minutes on each side for medium-rare. Toss the arugula with 1 tablespoon of olive oil and 2 teaspoons of vinegar.  Place the tuna steaks on a big service plate on top of the arugula and top with the salsa, making sure the juices from the salsa drizzle all over the tuna. Serve immediately.