Prep eggplant: Slice the eggplant into 1-cm (½-inch) thick slices. Salt both sides and set aside.
Make onion-ginger paste: Peel the onion, ginger, and garlic, and chop roughly. Blend in a food processor to form a paste (some small pieces are ok).
Cook mustard seeds & onion paste: In a deep pan or pot, heat 2 tbsp oil over medium heat. Add the mustard seeds and cover immediately. Once the mustard seeds have stopped popping, quickly add the onion paste (before the seeds burn). Cook 3 minutes.
Add spices: Add the other spices, and cook another 5 minutes, stirring occasionally to avoid burning.
Add liquids: Add the coconut milk, tomato paste, and ¾ tsp salt. Simmer while preparing the chard.
Chop & add veggies: Separate the chard leaves and stems. Chop the stems into ½-cm (¼-inch) pieces. Chop the leaves roughly, if using. Blot the eggplant dry, and chop into 1-cm cubes. Add the chard stems and eggplant to the pan. Simmer 20 minutes.
Add final veggies: Add the drained chickpeas and chard leaves (if using). Simmer another 5 minutes. The vegetables should be tender at this point.
Chop the cilantro leaves, including the smaller stems. Stir into the curry.
Make the topping: Stir the Greek yogurt and mango chutney together in a small bowl.
Serve: Serve the chard curry over rice or with an Indian flatbread. Top with any extra cilantro leaves and a scoop of the yogurt topping.