In a dutch oven, chop the cabbage that has been washed thoroughly and cored. Add the 1/2 cup of water to get the cabbage started boiling. Cover and let boil for about 5-7 minutes. Uncover and add the chicken broth, spices and sugar. Turn heat down to medium and cook for about 15 minutes. Add onion, green pepper and corned beef. At any stage that you may feel like the liquid is getting too low, you may add additional water to the dutch oven. Bring back to boil for another 15 minutes and turn back down on medium before adding the half and half. At this point, I perform a taste test for spices, doneness, and broth taste. Since the amounts would have to differ depending upon the amount of cabbage used-the recipe is most successful if it meets your taste standards.