Start by searing the ribs. Pat the short ribs dry and season the ribs on all sides with kosher salt and black pepper. Heat the olive oil over medium heat in a large, cast iron skillet. Add the short ribs to the skillet and sear, using tongs to turn the meat so all sides are browned, around 7-10 minutes total. Set aside. 

Place the shredded cabbage in a 12 quart stock pot. Use your hands to crush the tomatoes into smaller pieces, adding them to the pot along with the reserved tomato juice. Tuck the seared ribs into the cabbage and top with the sauerkraut.

Pour the beef stock into the pot and bring to a simmer. Reduce the heat to low, cover and cook for 1½ to 2 hours, or until the meat is tender and falling off the bone.

When the meat is thoroughly cooked, carefully use tongs to remove the meat and bones from the soup and set aside.

Add the hotdogs to the soup with the lemon juice. Season to taste with kosher salt and pepper and cook over low heat, covered, for another 15 minutes.

Meanwhile, shred the beef into bite sized pieces. Return the shredded beef to the soup pot. Serve hot, with crusty bread and additional lemons, if desired.