Prepare a shortcrust pastry from flour, chestnut flour, butter, sugar, salt and water. Line a greased baking pan with it and pull up the edges. Chill the pastry pan. Preheat the oven to 180 degrees. Clean the mushrooms and cut them into larger pieces.
Heat the butter and oil in a large pan. Sauté the onion and garlic until translucent. Add the mushrooms and thyme sprigs, season with salt and pepper and sauté for about 10 minutes. Remove the thyme and stir in the parsley and chives. Let the mixture cool down and then spread it on the dough base.
Whisk the eggs and crème fraîche with salt and pepper. Pour it over the mushroom mixture. Bake for about 45 minutes. Garnish with parmesan slices and a sprig of thyme.