Soak the meat in a couple changes of water for a few hours to reduce the salinity.
Place the pork in a saucepan. Cover with cold water and bring to a boil. Reduce heat and simmer. Simmer the pork until tender when pierced with a fork, about 2 to 3 hours.
In the meantime, boil the cabbage for 10 minutes in salted water. Drain well.
About 20 minutes before the pork is ready, add some of the pork cooking water to a level of about 1/4" to a separate saucepan. Bring to a boil. Add the butter and the cabbage. Cook the cabbage without letting it get mushy.
To serve, place a cabbage quarter on each serving plate. The core can be cut from the cabbage for a nicer presentation, if desired. Slice the pork and arrange alongside the cabbage.