Peel and devein shrimp. Cut salami in half lengthwise and then into 20-24 half moon slices. Thread shrimp, salami, and tomatoes on metal skewers, alternating and putting a piece of salami next to each shrimp. Grill, turning once, until shrimp are opaque.
Slice cheese and lay out on a platter. Drizzle with olive oil, balsamic, and salt and pepper. Remove skewers and distribute shrimp, salami and tomatoes over cheese. Chop basil leaves and sprinkle over the top.