Make the dressing first. In a small bowl combine the grated garlic cloves, light tasting oil, vinegar, sugar, and salt using a whisk. This will be the dressing.
Slice the eggplants into thick julienned sticks about 1 inch long. Place them into a colander and sprinkle 1 tsp salt over them. Let the cut eggplants sit for about 20-30 so they release their juices. Be sure to put a plate under to catch all the juices.
Place the eggplant into a single layer onto a baking sheet and lightly drizzle with olive oil. Toss the eggplant chunks around to evenly coat them in oil, then spread them out into a single layer again. Bake at 400 degrees Fahrenheit for 25 minutes.
Meanwhile, slice the onion into thin slices and submerge it into a bowl of cold water for about 10 minutes. This will help reduce that strong oniony taste. Once the 10 minutes are up, drain the water as best as possible.
Chop the cabbage into shreds. Then slice the carrot and bell peppers into julienned (match sticks).
Combine the chopped cabbage, carrot, bell peppers, sliced onion, and cooked eggplant in a larger bowl and set aside.
Add the chopped parsley to the bowl of chopped vegetables and pour the dressing over it. Generously toss the salad to ensure the dressing coats evenly. Serve chilled.