Peel and thickly slice the potatoes. Cook them in boiling, salted water for 10 minutes, until soft. Drain them and mash well.
Peel and finely chop or grate the onion. Chop the luncheon meat.
Mix together the potato, onion, luncheon meat, and bind together with the well-beaten egg, adding sufficient egg to hold it all together. Season with the salt, pepper, and herbs. Form the mixture into 3-4 equal portions. Shape each into a ball and then flatten to form 'beefburger' shapes about 3/4in (2cm) thick.
Heat the oil and butter in a frying pan, and fry over a moderate heat for 3-4 minutes, turning to cook both sides, until crisp and golden brown. Serve with fresh or fried tomatoes and/or a couple of fried eggs, if you're really hungry.