Chop the cooked meat into small pieces and place it in a large mixing bowl with the mashed potatoes. Roughly chop all the other vegetables you are using into small pieces and add these to the bowl. Add salt and freshly-ground pepper to taste, then mix well so that the meat, potatoes and vegetables are evenly dispersed. Using your hands, form the mixture into flat 'cakes' about 1" (2.5cm) thick and about 4" (10cm) round.
Melt a little duck fat, goose fat or beef dripping to a frying pan over a medium heat (you can use oil if you wish, but it lacks the flavour of any of the fats). Add the bubble and squeak 'cakes' and cook for about 5-6 minutes. Check the underside which should have formed a thin, golden-brown 'skin' and, if ready, turn over and cook the other side in similar fashion. (You may need to add a little more fat to the pan if the bubble and squeak is sticking). After a further 5-6 minutes, serve the bubble and squeak hot with lashings of ketchup.