Reduce the vinegar and sugar to a demi-glace. Set aside.
Blanch, peel, and coarsely dice the tomatoes.
Finely chop the onion and sauté it in a pan with a drizzle of olive oil until translucent. Add the tomatoes, cook for 5 minutes, and set aside to cool.
Cut each eggplant in half and then each half into 2cm thick slices. Season with salt.
Pan-fry the eggplant slices with a drizzle of olive oil until golden brown on both sides.
When serving, arrange the eggplant slices and place a spoonful of tomato concassé on each slice.
Add a few Parmesan shavings and some arugula leaves.
Season with fleur de sel, pepper, then drizzle with a reduced balsamic vinegar and a dash of olive oil.
Serve chilled.