I use pearl barley in this stew because it's always at my grocery store. I haven't tried this recipe with hulled barley yet, but I think it would work just fine. The long cooking time should work well with hulled barley, and the barley might hold its shape better than pearled barley. If you only have quick-cooking barley on hand, then I would cook the quick barley in a separate pot, then simply stir it into your stew after it's finished.