Heat the olive oil in a sauté pan. Sauté the fennel slices in it, then season with salt, pepper and sprinkle with sugar. Mix and fry over medium heat for 15 minutes.
Preheat oven to 180 degrees. Cover the baking pan with the fennel, sprinkle with the thyme and spread the parmesan shavings on top. Cover with the puff pastry and press the edges of the pastry into the mold. Bake for 25 minutes.
Take out of the oven and let cool for 5 minutes. Carefully turn the tart out onto a platter. Serve hot or lukewarm.