Put the crab meat in a medium bowl, add the mayonnaise and sour cream and mix together. Fold the tomatoes, artichoke hearts and scallions into the mixture. Add salt and pepper.
For a cold dip: Refrigerate the mixture until chilled, about 30 minutes. Serve with your choice of bread or crackers.
For a warm dip (our favorite): Preheat the oven to 325 degrees F. Transfer the mixture to a baking dish and top with the Parmesan. Bake until the cheese is melted, 10 to 15 minutes. Serve with your choice of bread or crackers.