Peel the garlic the day before. Core and wash the chillies. Chop both. Wash the lime and grate the peel. Squeeze the fruit. Wash thyme, dab dry, remove leaves. Mix prepared ingredients, rum, oil and 1 tablespoon sugar.
Split the legs in the joint, wash and pat dry. Pour the marinade over it, cover and leave to cool overnight.
Cover the potatoes and sweet potatoes and boil them in water for about 20 minutes. Roast sesame without fat. Mix yoghurt, tahina and lime juice. Season with salt, pepper and sugar. Drain, peel and dice the potatoes.
Mix with the sauce and let it stand for about 30 minutes.
Season the legs with salt and grill on the hot grill for 20-30 minutes, turning. Wash coriander, shake dry, remove leaves and fold into the salad. Sprinkle with sesame seeds.