Heat the oil in a large nonstick pan. Add the onion, chiles, and cumin, and cook until the onions are soft and beginning to color.
When the onions are cooked, stir in the carrots, potatoes, turmeric, and salt. Cover the pan and cook over a low heat, stirring often. If necessary, add a splash of water to prevent the vegetables from burning.
After about 15 minutes, add the cucumber and beans. Cover the pan again and cook for another 5 to 10 minutes, or until all the vegetables are tender.
Meanwhile, put the shallots, ginger, and coconut (complete with its soaking liquid) into a blender. Blend to a fine paste before adding to the pan, along with the peas. Cook for a further 5 minutes, stirring thoroughly. Tear the curry leaves into the pan, and stir in the yogurt.
To serve the dish, take the pan off the heat and pour the coconut oil over the vegetables, if using. Spoon the mixture on to 6 serving plates and serve with basmati rice.
NotesThis recipe is deceptively easy and adapts to most vegetables.