Clean and roughly chop the carrots and celery stick. Place them in a food processor and blitz until finely chopped. You can finely chop the carrots and celery by hand if you prefer.
Sauté the carrot and celery mix with the extra virgin olive oil, until soft and fragrant.
Add the meat and brown it well on all sides. Add the white wine, salt and pepper to taste.
Cover the meat with the sliced onions and cherry tomatoes and stir. Add enough water to cover the meat and onions, cover with a lid and cook, over a low flame, for at least 2 hours or until the meat is very tender.
When the meat is ready, remove it from the pan and set aside. When it cools down, slice it and serve it in a separate dish (it will work nicely in sandwiches).
Increase the heat and reduce the onion sauce until golden brown.
Using your hands, snap the ziti into 3 parts and cook the pasta al dente, following the instructions on the package.
Drain the ziti and mix in a serving bowl with the Genovese sauce. Grate over some Pecorino Romano and serve.
