Place smoked pork butt in a 6-quart pot with enough water to cover; season with salt and pepper. Bring to a boil over medium-high heat, then reduce heat to medium-low and simmer for 1 hour.
Stir in potatoes and cabbage. Simmer until potatoes are tender, about 20 minutes.
Remove pork from soup and cut into quarters; return pork to pot until ready to serve. Season with more salt and pepper, if needed.