Wash the eggplants and cut them into long slices about 3 to 4 mm thick.
Layer the slices in a colander.
Sprinkle some coarse salt over each layer. Press down firmly.
Place a plate on top of the eggplant slices and put a weight on it, such as a heavy glass jar. This will draw moisture out of the eggplants. Let it rest for 1 hour.
Preheat the oven to 200 ยฐC.
Rinse the eggplants well to remove the salt.
Pat the eggplants dry with paper towels.
Line a baking sheet with parchment paper. Drizzle the parchment paper with olive oil.
Pick the leaves from 2 sprigs of thyme and sprinkle them over.
Place the eggplant slices on the baking sheet and drizzle them with olive oil. Season with fleur de sel, pepper, and thyme sprigs.
Put the baking sheet in the oven for 20 minutes.
Make the tomato sauce. Peel the garlic. Heat the olive oil in a pot and press the garlic into the pot. Let it sautรฉ briefly.
Add the tomato passata.
Coarsely chop the basil leaves and add them, along with the sprigs of thyme, oregano, and bay leaf. Season with pepper and salt.
Let it simmer for 10 minutes. Remove the bay leaf.
Grate the Parmesan. Cut the provolone into 4 pieces and then into slices.
Spoon some tomato sauce into the bottom of 4 small ovenproof dishes.
Place eggplant slices in the ovenproof dishes.
Cover with half of the provolone.
Spoon some tomato sauce over the cheese.
Add another layer of eggplants, provolone, and the rest of the tomato sauce in the dishes.
Finish with the Parmesan.
Put the ovenproof dishes in the oven for 20 minutes. Serve warm.