Shred the cabbage and julienne the carrot (cut into thin slivers). Combine in a bowl with the mayonnaise, ginger and garlic and mix well.
Heat the butter in a medium skillet over a medium flame. Add the raisins and cook until soft and golden brown, about 2 minutes. Mix the warm raisins into the slaw and add the vinegar and salt, sugar and pepper to taste. Cover and refrigerate until ready to serve.