Place the smoked pork into large pot and fill with 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 the carrots, potatoes, cabbage, and onions. Cover and continue to simmer. Use kitchen string to tie the green beans into a bundle. Add them to the pot. Cover, and continue to cook until the carrots are tender, about 25 minutes.
To serve, remove pork to serving dish. Arrange vegetables around it. Allow pork to rest about 10 minutes before slicing.