Through the feed opening of a running blender, add 1 at a time, the vinegar, shallot, garlic, salt and pepper. Then, leaving the blender running, add the olive oil in a thin stream. Set aside until needed.
Toss together the lettuce, cabbage, and cucumbers with enough of the dressing to coat, and gently fold in the tomatoes. Serve family style with additional dressing on the side.