To make the sauce, combine brown sugar, soy sauce, garlic, and ginger. Set aside.
Cut eggplant lengthwise into 1/2-inch slices.
Using a sifter, sprinkle cornstarch over both sides of the eggplant slices.
Add half of the olive to the skillet and heat over medium-high until shimmering.
Add eggplant slices, taking care not to crowd them too much. Cook 3-4 minutes. You may need to cook in batches.
Add remaining olive oil to the pan, then flip the eggplant slices over and cook an additional 3-4 minutes.
Reduce heat to low. Add sauce to the pan and flip eggplant to coat. You may have to flip several times to get both sides coated. Remove from pan and serve over rice.