Heat the vegetable oil in a large deep skillet over medium heat. Add the chopped onions, sprinkle with ¼ teaspoon salt, and cook for about 5 minutes, stirring occasionally.
Add the chopped celery and bell pepper to the onion mixture and continue cooking, stirring occasionally, for 7-8 minutes.
Add the ground beef to the mixture in the skillet and season it with 1 teaspoon of Cajun seasoning. Using the side of a wooden spoon or spatula, break the beef up into small portions. Continue breaking it up, flipping it in the skillet, and stirring it occasionally until the meat has browned, about 10 minutes. Add the minced garlic to the beef mixture in the skillet and cook 1 minute.
Add the chopped eggplant and ½ cup water to the beef mixture. Stir to incorporate the eggplant pieces into the beef mixture. Cover the skillet and lower the heat to simmer.
Every 15 minutes or so, stir the mixture to coat the eggplant with any liquid in the skillet. Bring the eggplant pieces around the perimeter of the pan to the center and move the pieces from the center to the edges. Continue cooking the eggplant mixture over low heat this way, adding ¼ cup of water at a time when necessary for 1-2 hours.
During the last 30 minutes of cooking the eggplant dressing, make the rice.
To check if the dressing is done, press on the eggplant pieces to see if they have collapsed into very soft texture. If so, press on them with the back of spoon to mash them up a bit.
Fluff the rice with a fork and add to the eggplant mixture. Stir to combine well. Taste for seasoning and add more salt, pepper, dried basil, or Cajun seasoning if desired.
Right before serving, add the chopped parsley and basil leaves to the dressing. Stir to distribute well.
Serve with Tabasco Green Pepper Sauce, if desired.