Heat 2 tablespoons of the oil in a large pan over medium-high heat. Add enough eggplant to form a single layer in the pan, and cook, stirring often, until well browned, 8 to 10 minutes. Tip the eggplant into a large bowl and repeat with the remaining eggplant, adding additional oil as needed until it is all browned. Set aside. Add 1 tablespoon of oil to the pan. Add the potatoes and cook, stirring often, until golden brown, 5 to 7 minutes. Transfer the potatoes to the bowl with the eggplant and set aside.
Heat a dry large pan over medium heat, add the cumin, mustard and fenugreek seeds and toast until fragrant, 1 to 2 minutes. Add 1 tablespoon of oil and when hot add the onion, curry leaves, and ¾ teaspoon salt, or to taste, and cook, stirring frequently, until soft and golden, 7 to 10 minutes.
Add the tomato paste and cook for 2 minutes. Add the garlic, ginger, turmeric and tomatoes and cook until the tomato juice has evaporated and the mixture is starting to dry up in the pan, 10 to15 minutes.
Meanwhile, in a medium pot, bring 2½ cups (600 ml) water and a pinch of salt to a boil over medium heat. Add the rice, reduce the heat slightly, cover and boil for 10 minutes. Remove the pot from the heat, keeping the lid firmly on, and set aside for 10 minutes.
Add the eggplant and potatoes to the curry pan, along with the remaining ¾ cup (200ml) water. Bring to a boil, reduce the heat to medium-low, cover and simmer for 15 minutes, stirring occasionally. Remove the lid and simmer until the vegetables are tender, 35 to 45 minutes. Stir in half of the chopped cilantro and adjust salt to taste.
Remove the lid from the rice and fluff up with a fork. Serve alongside the curry, sprinkled with the remaining cilantro.
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