Source: Smitten Kitchen, where it was adapted from Bobby Flay
Blend green onions, vinegar, chiles, mayonnaise, oil, salt, and pepper in a blender or food processor until emulsified. Place cabbage and red onions in a bowl, add the dressing, and toss until combined. Fold in the cilantro and season with salt and pepper to taste.
The purple cabbage is hardy, and thus holds up fairly well to the dressing. We ate slaw that had already been dressed the second day as leftovers, and it wasn't too watery or soggy. However, the flavor and crunch is always best if you mix the cabbage/onions and dressing together just before serving, and mix just enough for the meal of that day.