To prepare the curry, heat the olive or coconut oil in a large pot or Dutch oven over medium heat. Add the onion. Cook the onion until it's clear and tender, about 5 minutes. Add the garlic. Continue cooking the garlic for 1-2 minutes, or until it's very fragrant. Stir in the cumin, curry, turmeric, garam masala, and salt, as well as a few tablespoons of water, to help mix everything together and create a kind of slurry.
Add the eggplant, tomatoes, chickpeas, and broth. Bring the mixture to a boil and reduce it to a simmer. Cover and cook for fifteen minutes. Uncover the curry and cook it for another 15-20 minutes, or until the liquid has reduced and the eggplant is melt-in-your-mouth soft. Check the mixture and adjust seasonings to taste. Divide the curry into bowls and serve over a cooked whole grain or with flatbread. Directly before serving, sprinkle each bowl with a tablespoon or two of parsley or cilantro. Curry leftovers will keep in an airtight container in the fridge for up to four days.
To make the flatbread, whisk together the chickpea and rice flour, salt, and cumin in a medium or large mixing bowl. Add the warm water and whisk until you have a smooth batter, making sure to catch any lumps. (To make super easy work of this, use an immersion blender or a regular blender instead of a whisk.) Then, stir in the parsley. Cover the bowl and allow the batter to rest for 30 minutes, or transfer the batter to an airtight container and let it rest in the fridge for up to 24 hours before you make the flatbreads.
Heat a small amount of olive oil (about a teaspoon, or use a mister or spray oil for convenience) in a medium sized frying pan or skillet (I used a pan that was about 10 1/2 inches across at the top and 8 inches across at the bottom, but I could have used something even a bit smaller) over medium heat. Add the batter to the pan by the heaping 1/3 cup. Allow the batter to cook until small bubbles are forming evenly across the top, and then gingerly use a spatula to loosen the flatbread from the pan and flip it. Continue cooking the other side for 1-2 minutes, or until it's cooked through and can be easily removed from the pan. Continue this process with all of the remaining batter. As with pancake-making, the flatbreads will probably get more consistent as you continue to use up the batter with confidence!
Serve the flatbreads with any soup, stew, or curry, or enjoy them with hummus spread on top. They're versatile. If you'd like to make a simpler version, you can omit the parsley and cumin. The flatbreads will keep in an airtight container in the fridge for up to three days.