Make the pesto sauce in a blender or food processor. First put the chestnuts, garlic and cheese and beat well. Add the ice, leaves and oil and beat until smooth. Do not overdo it, as the blade oxidizes the leaves.
Cut the tomatoes and mozzarella into slices of the same thickness, about 1 finger.
You can assemble it in layers vertically or horizontally, interspersing the tomatoes with the mozzarella, adding a basil leaf. Season with fleur de sel, sprinkle with pesto sauce and drizzle with a drizzle of olive oil.