Heat your oven to 180°C/Fan 160°C/Gas 4. Scrub and slice the sweet potatoes as thinly as possible. Lay the slices in a medium-sized baking dish.
Finely chop the chilli, flicking out the seeds for a milder heat. Peel and grate the ginger and garlic. Zest and juice the lime. Roughly chop the coriander stalks, saving the leaves for later.
Tip the chilli, ginger, garlic, coriander stalks, lime zest and half the juice into a food processor. Squeeze in the curry paste and peanut butter. Pour in the coconut milk. Blitz to combine. Taste and season.
Pour the fragrant coconutty sauce over the sweet potato slices. Tumble together with your hands, then spread out.
Cover the dish with foil and seal the edges tightly. Cook for 30 mins. Remove the foil and cook for a further 20 mins till golden. Check the sweet potato is done by piercing with a knife. If still firm, return to the oven and cook for another 5-10 mins.
Whisk the remaining lime juice with 1 tbsp oil and some seasoning. Quarter the tomatoes. Toss the tomatoes and lamb's lettuce with the dressing. Serve with the sweet potato gratin, garnished with chopped coriander leaves.