Place a large pot of water over high heat and bring up to a boil to cook the pasta. Once the water comes to a boil, add a generous amount of salt and cook pasta until al dente according to package directions.
While the pasta water is coming up to a boil, start the sauce: Heat a large skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add garlic, bay leaf and allspice, and cook until golden. Add the chopped, leftover brisket and vegetables. Stir and cook for a few minutes to heat everything through. Add the crushed tomatoes, bring up to a simmer and cook for 5 minutes.
Drain the pasta and toss with the sauce. Add the parsley and serve, passing grated Parmigiano Reggiano at the table.