I always cook up two pieces; both a flat brisket and a tip. The brisket is good for Reuben sandwiches, the tip goes into what I call Reuben soup. Instead of using plain cabbage in the original dish, I toss in a can of kraut. I chop the leftovers quite finely and turn the leftovers into soup. On a cold day taken with a slice of Swiss on a slab of rye you have a real tummy warming meal.
By the way, to make the broth more easily eaten, I cook the meat first, with lots of extra spices (whole mustard seed, bay leaf, peppercorn, allspice, juniper berries, and a few cloves) in addition to the little packet that comes with the meat. Then I take the meat out, scrape of most of the spices, strain the broth. Refrigerate overnight to de-fat in the morning, then put it all back in with the carrots potatoes, more onions, and cook.
I have an elderly friend with no teeth, so when I make soups she gets first dibs, and this is a favorite.