Turn on the blender and while it's running, add one at a time through the feed tube, the vinegar, fresh ginger, garlic, parsley and mayonnaise, and blend together until a smooth paste has formed. With the power still on, pour the olive oil in a thin stream through the blender feed opening. Adjust the seasoning with salt and pepper,
Toss together apples, cabbage and onion, and stir in enough of the dressing to coat. Gently fold in most of tomato wedges, reserving some for garnish. Taste and adjust seasoning (salt and pepper) if necessary. Serve chilled, garnished with reserved tomato wedges, and with the remaining dressing on the side.