In a wide cooking pan(10 inch or larger) or wok, heat up the oil. If you are using mustard oil you will need to heat it up for up to 1-2 minutes to do away the raw smell. Make sure that the oil is not smoking.
Once the oil is hot, reduce the heat to low, wait a little and then temper hot oil with dried chili, hing, fenugreek and cumin seeds. Let crackle. Immediately add the garlic (chopped fresh garlic is best). Let cook for 5-7 seconds taking care they do not burn. (You do not want the garlic to turn bitter as it changes the taste of the sabji, take the pan off the heat, if needed).
Add the potatoes next and sprinkle a little salt. Let them lightly brown in hot oil for 2-3 minutes.
Next, add a splash of water and sprinkle spice powders- coriander, red chili and turmeric. Fry for 1 minute taking care that ground spices dont burn.
Pour in the tomato puree next. Mix well and then cover the pan. Let cook on low- medium heat till the potatoes are 50%-60% tender. The moisture from tomatoes should be enough to par cook the potatoes. However, make sure to check in between and add a splash of water if needed
Meanwhile, wash the eggplant and cut it up roughly the same size as the potatoes.
To the par boiled potatoes, add the chopped eggplant and salt. Mix well so that everything is covered in spices & tomatoes. Fry for a minute or two to get the eggplant started, it will start releasing its juices.
Cover again and let cook till both eggplant and potatoes are tender. On medium low heat this should take 7-10 minutes. Cook time will depend on the variety and size of the vegetables. As the eggplants cook, they will release their water and that should be enough to cook everything.Check 1-2 times while cooking to make sure that the sabzi isn't getting dry else add ¼ cup to ⅓ cup water water. Note on Cooking Time - We don't like mushy potatoes or eggplants so I have noted the cooking time accordingly. If you prefer softer or mushy eggplants and potatoes, cook longer (about 5-7 minutes extra) to achieve the desired softness. Take off the lid and sprinkle the amchur powder, garam masala and crushed kasuri methi. Instead of amchur, you can use teaspoon of lemon juice. At this stage you can also add some chopped green chilies. On high heat, gently toss (vegetables are very soft right now!) everything for another 1-2 minutes. Garnish with chopped cilantro & serve.