Heat half of the olive oil in a large heavy-based stockpot (preferably cast iron) over medium heat. Add the diced pancetta and chilli, then cook until golden and crisp (approximately 4 minutes). Set the pancetta and chilli aside on a plate.
Heat the remaining olive oil in the stockpot. Add the garlic and onion. Cook until the onion is tender (about 4 minutes). Add the carrots and celery. Cook for 5 minutes, continually stirring until the vegetables have softened. Return the pancetta and chilli to the stockpot with vegetables. Season with salt and pepper to taste.
Stir the tomato paste into the vegetables. Cook for 2 minutes, stirring continuously then add the tripe. Pour over the white wine and cook for 5 minutes or until slightly reduced. Add the hot chicken stock, then reduce the heat to low. Cover and cook for a further 1 hour or until the tripe is tender.
Note: The Tripe you buy in Australia and around the world is usually partially pre-cooked, but still needs to be cooked further. Tripe varies in the amount of time it has been pre-cooked so ask your butcher what the recommended cooking time is for the tripe and use this as a guide.
Stir parsley through the Trippa alla Romana (Roman-style tripe). Serve immediately, topped with a generous grating of Pecorino Romano on top – buon appetito.