Put the potatoes into a large pan of boiling salted water and cook for 3-4 minutes, or until almost cooked, but still a bit firm in the middle. Drain well and leave to cool.
Heat the oil in a large frying pan. Add the potatoes and fry over a medium heat for about 5 minutes, turning from time to time until a light golden brown. Sprinkle over the cumin seeds and diced chili, and continue to fry for 3-4 minutes.
Stir in the ground cumin, cayenne and turmeric. Fry for another 5 minutes, tossing and turning the potatoes until they build up a nice spicy crust. Season before serving, dusted with garam masala.