First make the dressing: put lemon juice with sesame paste, olive oil and garlic in a blender and process very smoothly. Season to taste with salt, pepper, cayenne pepper and sugar.
Peel the eggplant if you like (I don`t usually do it, but the skin of the large eggplants can sometimes be bitter) and cut into 1-cm cubes. Mix the cubes with the olive oil and garlic and season with salt and pepper. Spread the vegetables out on a baking sheet with a rim and roast them in the oven for 15 to 20 minutes, until the cubes are soft but not yet disintegrated.
Mix with the dressing while still warm, season to taste again.
The vegetables are best when they are lukewarm; it goes particularly well with lamb chops and tomato slices.