Heat oil in a frying pan for deep-frying. Place potato starch in one small bowl and beaten egg with a dash of salt in another. Dip eggplant slices in egg and then potato starch and fry for two minutes on each side. Drain on paper towels.

Using fresh oil, sauté diced red onion for five minutes. Add the cherry tomatoes, garlic, and salt, and sauté an additional five minutes. Add carrot sticks and sauté another three minutes. Remove from heat and separate the carrots from the rest of the mixture.

Arrange salad greens on a plate. Place an eggplant disc on top. Place a spoonful of the tomato-onion mixture on top and arrange three carrot sticks like a fence around the eggplant disc. 

Serve at room temperature, or rewarm just the discs on a baking sheet in a 275°F (140°C) oven.