Place smoked ham or pork shoulder into a large pot and add enough water to cover. Season with salt and pepper, cover, and bring to a boil. Reduce heat to low and simmer for about 30 minutes.

Add potatoes, cabbage, onions, and carrots to the pot and continue to simmer. Tie green beans into a bundle with kitchen string. Add to the pot, re-cover, and cook until carrots and potatoes are tender, about 25 minutes.

Transfer pork to a serving dish and arrange vegetables all around. Let pork rest for 10 minutes before slicing and serving.