Preheat the grill to medium-high.
Place the tomatoes on the grill and roast, turning, until the skin is evenly charred. Remove and when cool enough to handle, peel and seed the tomatoes.
Place the tomatoes in a blender or food processor, and process with the oil and vinegar. Season, to taste, with salt and pepper. Add the basil, and adjust the seasoning, to taste. Serve warm with the grilled soft shell crabs.
Yield: about 3 cups