While it is a great idea to toss leftover brisket from your weekend bbq with pasta, it will definitely take on a very different flavor profile than this recipe. Here, the instructions are for slow cooking raw brisket over several hours. Leftover brisket is already cooked, so it just needs to be heated up, not braised for several hours.   Having said this, if you have leftover, cooked brisket, you can incorporate it into the spirit of this recipe. I would suggest sautéing some carrots/onions/celery/garlic as indicated, deglazing the pan with red wine, let the alcohol taste cook off, then add the brisket and let it simmer in the mixture for about 20 minutes. Add some broth for additional moisture and to create more of a sauce. Then, fold in some cooked pasta, top with grated cheese and olive oil and enjoy!