To make the Mediterranean eggplant roll-ups, first prepare the sauce: heat the olive oil in a small saucepan, add the garlic clove, and gently sauté over low heat for about 5 minutes. Once the oil is fragrant, pour in the tomato purée, season with salt and black pepper, and let simmer for another 15 minutes.
While the tomato sauce is cooking, wash the eggplant and cut it lengthwise into slices about 1 cm (0.4 in) thick using a mandoline to obtain 4 uniform slices. Heat a grill pan well and grill the eggplant slices on both sides until tender, then transfer them to a plate or cutting board.
When the tomato sauce is ready, remove and discard the garlic clove. Tear the mozzarella into small pieces by hand and preheat your oven to 180°C (350°F) in static mode.
Assemble the roll-ups: spread a thin layer of tomato sauce over the surface of each eggplant slice, add some torn mozzarella, a teaspoon of olives, and a fresh basil leaf.
Roll up the filled eggplant slices and arrange them seam-side down in a small baking dish.
Spoon a little tomato sauce over the roll-ups and top with the remaining pieces of mozzarella.
Bake in the preheated oven for about 10 minutes, just until the cheese has completely melted. Once out of the oven, serve your Mediterranean eggplant roll-ups hot and stringy!