Put the finely diced celery, carrot, onion and potato in a saucepan, add the grated ginger and a tablespoon of miso. Bring to the boil mixing every so often, and let it reduce until it is a creamy sauce. If needed, use a stick blender.
In the meantime, sauté gently the garlic in the olive oil in a saucepan. When the garlic is golden, remove and add the cherry tomatoes, a ladle of water, salt, basil and simmer gently, covered for about 10/15 minutes.
Slice the eggplants into rounds, of at least 8 slice s, each ¼ inch thick. Put them on an oven tray and with a knife, make small diamond-shaped cuts in the eggplant flesh. Season with salt, herbs and chili pepper, and drizzle with extra virgin olive oil. Bake in the oven at 400F for 30 minutes.
As soon as the eggplant slices are cooked, take them out of the oven. Cut the mozzarella into 4 slices and place on top of 4 eggplant slices and then cover with the remaining 4 eggplant slices to form a sort of sandwich.
The dish must be served hot. Put the miso sauce on the bottom of each plate, place the aubergine sandwich on top and cover with the cherry tomato sauce; garnish with a sprinkling of sesame seeds.