For the tart
In a medium sauté pan, heat the olive oil. Sweat the leeks until wilted and translucent, about 15 minutes. Add the mushrooms season with salt and cook until the mushrooms soften and most of the liquid has evaporated. Remove from the pan mix in the thyme and let cool to room temperature Combine the eggs, cream and yoghurt in a bowl season with salt and pepper and whisk them together. Place the leek –mushroom mixture in the prebaked shell in an even layer. Pour the cream mixture over the leeks and bake at 180⁰C until a knife blade inserted in the center comes out clean, 40 to 45 minutes. If the pastry begins to overbrown, cover the edges with strips of aluminum foil. Remove the tarts from the oven and cool on racks. Let the tarts rest for at least 20 minutes before cutting. Serve hot, warm, or at room temperature.