Cut the aubergine into slices, season with salt and let it steep. Then dab and dice. Peel and halve shallots, depending on size. Sear the carrots in a little olive oil, then season. Caramelize with 1-2 teaspoons of sugar. Deglaze with balsamic vinegar and cook until al dente. Set aside in a bowl.
Do the same with the other vegetables in the same pan. Let all vegetables steep for at least 3 hours, then arrange on a platter. Possibly Drain off excess liquid (this is often the case with zucchini).