Preheat oven to 200C. Combine oils, ginger, spices, lime juice and garlic in a bowl and season to taste. Add chicken, mix well to coat and stand for 10 minutes to lightly marinate.
Meanwhile, for salad, heat oil in a frying pan over medium-high heat, add chilli and curry leaves and fry until fragrant (30 seconds). Remove from heat and stir in garlic. Tip into a large bowl, add chickpeas, carrot and lime juice, season to taste and toss to combine. Just before serving, add coriander and toss together.
Heat a large frying pan over medium-high heat, add chicken skin-side down and cook until browned and fat renders (4-5 minutes). Turn and brown the other side (1-2 minutes). Transfer to an oven tray and roast until cooked through (3-4 minutes). Serve hot with carrot, chickpea and coriander salad, and yoghurt.