Preheat oven to 200°C/180°C. Carefully cut 3mm slices into the sweet potatoes, leaving 5mm intact at the bottom. Place on a baking-paper lined oven tray.
Strip the leaves from the thyme and tuck in between the fans of the sweet potatoes.
Drizzle with oil and sprinkle with salt. Sprinkle with salt and pepper, then drizzle with olive oil.
Bake for 1 hour - 1 hour 10 minutes until golden and soft in the middle, or when easily pierced with a knife. Serve sprinkled with parmesan.