1. The dough: quickly mix the flour, salt, and oil with softened butter until it forms a smooth paste.
Add a splash of water to bind the dough together (if it's too sticky, add more flour), and let it rest for 1 hour if possible.
2. Filling: roll out the dough in a floured dish, sprinkle the bottom with grated Parmesan, then spread half of the eggplant slices (even if they're just taken out of the freezer!).
3. Cut the eggplant, tomatoes, and mozzarella into thin slices.
4. Sprinkle half of the tomatoes and mozzarella on top, season with salt and pepper, and repeat the process.
Sprinkle with Herbes de Provence.
5. Finish with a drizzle of oil over the entire tart, then sprinkle with Parmesan.
6. Bake for 20 minutes at 6/7 thermostat (200°C), and serve warm or cold.