Preheat the oven to 220C/200C fan forced. Line the base and side of a 26cm (base measurement) ovenproof frying pan with a disc of baking paper.
Sprinkle the base of the pan with the thyme sprigs, then top with the parmesan. Use a fork to spread evenly. Arrange the potato halves on top, cut-side down, in a circular pattern. Drizzle with oil and season with pepper.
Bake for 40 minutes or until the potato and parmesan are golden. Sprinkle with extra thyme leaves and season with salt, to serve.
