Dice the potatoes into 1cm chunks. Cook the onion until soft, add the garlic and cook for a further three minutes. Mix in the chorizo and potato, turn up the heat and fry for another five minutes. Mix in the thyme and season. Assemble all the rest of the quesadilla ingredients.
Spread a quarter of the chorizo mixture on one half of a tortilla and sprinkle with a fistful of cheese. I find that a mix of extra mature English Cheddar and a little grated mozzarella makes the perfect cheese mix, with a good flavour and the right gooeyness.
Fold the tortilla over so that you have a half moon. Brush it with a little olive oil (so the tortilla doesn't stick to the pan) and place in a hot, dry frying pan or griddle and cook until golden and crisp. Repeat with the remaining tortillas.
Cut into wedges and serve with your favourite table salsa.