The sweet smoky flavor of a ham shoulder, shank or butt end pairs well with the earthy pungent taste of cabbage, and both can be cooked together as part of what is sometimes called a "New England boiled dinner." The meat is first cooked alone to release its flavors and to leach out some of the fat and salt, then the cabbage, along with other vegetables such as potatoes, carrots, turnips and celery, are added during the second boil. The result is a one-pot meal that calls for no other side dishes other than perhaps a freshly tossed salad or creamy cole slaw.
Remove all the packaging from the ham and place it in the stockpot or Dutch oven. Fill the pot with cold water to about 2 inches over the top of the ham, cover the pot and set it on a burner set to high heat. Bring the water to a boil and cook the ham for 2 to 3 minutes. Turn off the heat, use the forks to remove the ham from the pot and drain off all the liquid.
Return the ham to the pot and place it again over high heat. Add fresh water to the pot to come to just about 2 inches over the top of the ham and add whole peeled onions.
Cover the pot and bring the water again to a rolling boil, then reduce the heat to medium or medium-low to maintain a steady simmer. Cook the ham for about 30 minutes for each pound of weight and add more boiling water to the stockpot any time it evaporates to below the top of the meat. Turn the meat over in the water once about halfway during cooking to assure even heating.
Add cored wedges of cabbage along with the peeled and cut potatoes and carrots to the pot during the last 30 to 40 minutes of cooking, and simmer until the vegetables are tender or to your liking. Turn off the heat and remove the ham and the vegetables to a serving platter.