Cut a criss-cross pattern into the eggplant, but be sure not to cut right through. Place the eggplant into a casserole dish.
To make the pesto, add basil, vegetable oil, garlic, salt, and pepper into a bowl and purée everything. Spoon the pesto into the gaps between the eggplant cubes.
Cut the cherry tomatoes and the mini mozzarella balls into thin slices, place them on top of each other, and insert them into the gaps.
To finish, sprinkle the grated mozzarella over the eggplant and bake it at 360°F for 40 minutes.