Put the mince, hamburger seasoning mix, Worcestershire sauce, tomato sauce and salt and freshly ground black pepper into a bowl. Knead the mixture with your hands until well combined. Cover with plastic wrap and allow to stand for at least 5 minutes to allow the flavours to meld together.
Divide the mixture into four and shape each portion into a flat patty. Using your thumb, make a deep hole in the centre of each patty, taking care not to push all the way through to the other side.
Place a quarter of the cheese (about 1 ½ tablespoons) into the centre of each patty, then mould the mince over to cover the cheese. If necessary, press flat.
Heat the oil in a large frying pan. Add the patties and cook over a moderate heat for 5–7 minutes on each side, or until cooked through. Serve with tomato sauce.