Preheat the oven to 190°C (375°F), Gas Mark 5. Place the chillies, shallots, garlic, lemon grass, galangal, turmeric, cayenne, coriander, cumin, cinnamon, fish sauce, sugar, lime leaves, coconut milk and lime juice in a food processor, and blend until fairly smooth.
Arrange the chicken drumsticks in a single layer in an ovenproof casserole. Scatter over the potatoes. Pour over the spice paste to coat the chicken and potatoes evenly. Cover and cook in the preheated oven for 40–45 minutes until the chicken is cooked through and the potatoes are tender. Serve hot, garnished with basil and chopped red chilli.