Cut the pork ribs into three or four pieces each. Salt and pepper. Place into a 6 quart pot with the melted butter and cook about 10 minutes, stirring frequently.
Add the chopped onion and sliced garlic until the onion is translucent. Add the balsamic vinegar.
Add the can of tomatoes and 1 can of water to the pot. Add the next 8 ingredients. Simmer on low until the pork is no longer pink, approximately 45 minutes.
Add the potatoes and carrots. Continue to cook at a low simmer for another 45 minutes or until the potatoes and carrots are done. If necessary, add another cup or two of water as needed. Add the cabbage to the top of the stew and steam approximately 15 minutes. Carefully stir the ingredients to mix thoroughly without crushing potatoes.
Serve with a pat of butter on the top of the stew.