Combine the Genoa and sopressata salami, provolone, mozzarella, tomatoes, and artichokes in a bowl. Slice the roasted red peppers and add them to the bowl, along with about 3 tablespoons of their juice.
Mix in the chopped olives. Drizzle olive oil over the entire dish, followed by the red wine vinegar and black pepper. Salad can be made ahead of time and refrigerated until serving.
Tear the fresh basil leaves into bite-sized pieces and add them to the salad just before serving. Mix thoroughly and serve.