Soak the barley in water for 6 hours or overnight.
Melt the butter in a large heavy pot over medium-low heat. Add the ham; cook until the edges turn golden, about 5 minutes. Stir in the garlic; cook 3 minutes longer. Add the carrot, parsnip, rutabaga, leek and cabbage. Cook, covered, 10 minutes. Add the chicken stock and heat to boiling. Reduce the heat and simmer, partially covered, 30 minutes. Add the barely and cook for 15 minutes more
Reduce the heat to low, and slowly stir the cream into the chowder. Warm the chowder through, but do not allow it to boil. Add salt and pepper to taste, the thyme, and the nutmeg. Just before serving, sprinkle the surface of the chowder with cheese. Serves 6 to 8.