Heat the vegetable oil in a large pan or skillet over medium heat. Add the mustard seeds and cumin seeds. Allow them to sizzle and pop for a few seconds.
Add the chopped onions to the pan and sauté until they turn translucent and slightly golden. Stir in the minced garlic and chopped green chili pepper, and cook for an additional minute.
Add the diced eggplant to the pan and stir well. Cook for about 5 minutes until the eggplant starts to soften.
Now, add the diced tomatoes, turmeric powder, paprika, ground coriander, ground cumin, and red chili powder (if using). Mix everything together until well combined.
Reduce the heat to low, cover the pan, and let the chutney simmer for about 15-20 minutes, or until the eggplant is fully cooked and tender. Stir occasionally to prevent sticking.
Once the eggplant is cooked, add the brown sugar (or sweetener of choice), apple cider vinegar (or lemon juice), and salt to taste. Stir well to incorporate the flavors.
Continue cooking the chutney uncovered for an additional 5 minutes, allowing the excess moisture to evaporate and the flavors to meld together.
Remove the pan from the heat and let the chutney cool to room temperature. Garnish with fresh cilantro leaves.
Serve the vegan Eggplant and Tomato Chutney as a dip with crackers, as a side with vegan curries, or as a condiment for sandwiches and wraps. Enjoy its rich and tangy flavors!