Put the eggplant chunks in a colander with a bowl beneath and sprinkle on the salt. Allow the eggplant to rest for about 30 minutes, then rinse well and pat dry.
Heat 1/4 cup of olive oil in the pot and fry the eggplant chunks until they turn light brown. Remove the eggplant and set aside.
Heat 2 tablespoons of olive oil in the pot, and sauté the onions until they turn soft and translucent. Add the tomatoes, kosher salt, pepper, parsley, mint, and eggplant. Stir and bring to a boil.
Pour the rinsed rice over the eggplant mixture and add the water, making sure the rice is fully immersed. Cover and bring to a boil, then reduce heat to low and cook with the lid on for 30 minutes. Turn off the heat, remove the lid, and lay a paper towel across the pot, then put the lid back on. Allow to rest for 10 minutes.
Turn out into a large serving bowl with the vegetables on top. Add a dollop of low-fat or fat-free Greek yogurt on top of each serving.