Heat olive oil in a saucepan over medium heat. Cook and stir onion, carrot, and garlic until onion is golden, about 5 minutes. Add tomatoes, sugar, salt, and pepper. Bring to a simmer; turn heat down to low. Continue simmering, stirring occasionally, for 10 minutes.
Meanwhile, heat vegetable oil in a separate pan over high heat. Fry eggplant slices in the hot oil until lightly browned, about 2 minutes per side. Drain eggplant slices on paper towels.
Mash the tomatoes in the saucepan using a fork for a less chunky texture. Remove from heat. Add eggplant and olives; stir gently to incorporate.
