Preheat the oven to Gas Mark 7, 220ºC, fan 200ºC. Simmer the potatoes in salted water for about 12 minutes, until almost cooked through. Test by piercing with a sharp knife. Drain thoroughly in a colander and return them to the saucepan, shaking vigorously to fluff up the potato edges.
Pour the oil into a roasting tin and put in the hot oven to preheat for 5 minutes. Scatter the semolina and Parmesan over the potatoes with a pinch of salt and gently turn with a spoon to coat evenly. Carefully spoon them into the hot oil, turning to coat, and roast for 40-45 minutes until gold and crunchy. Serve immediately, while still piping hot.