Cut the potatoes in half and cook them in lightly salted water for 20 minutes, until tender. Drain then cool them, then cut them into about 1 cm slices.
Thinly slice the onion & chorizo, then chop the garlic.
Heat the oil in a frying pan. Fry the onion, garlic and thyme in hot oil until soft. Add the potato slices and fry them until golden. Transfer them to a plate.
Fry the chorizo, until golden and has released its fat. Return the potato mixture to the frying pan and combine with the chorizo fat.
Add the parsley and serve.