How to Make It
Preheat the oven to 325°. In a very large skillet, heat the oil. Add the oyster and white mushrooms, season with salt and pepper and cook over high heat, stirring, until starting to soften, about 5 minutes. Reduce the heat to moderate. Add the butter, shallots and thyme and cook, stirring often, until the mushrooms are tender, about 12 minutes longer. Season with salt and pepper and let cool.
Scatter 1/4 cup of the cheese and half of the mushrooms evenly over the bottom of the Buttery Pastry Shell. In a blender, mix half each of the milk, cream and eggs and season with 1 1/2 teaspoons of salt, 1/8 teaspoon of pepper and a pinch of nutmeg at high speed until frothy, about 1 minute. Pour the custard into the pastry shell. Top with another 1/4 cup of cheese and the remaining mushrooms. Make a second batch of custard with the remaining milk, cream and eggs, plus the same amount of salt, pepper and nutmeg as before and pour into the shell. Scatter the remaining 1/4 cup of cheese on top.
Bake the quiche for about 1 1/2 hours, or until richly browned on top and the custard is barely set in the center. Let cool in the pan until very warm.
Using a serrated knife, cut the pastry shell flush with the top of the pan. Carefully lift the springform pan ring off the quiche. Cut the mushroom quiche into wedges, transfer to plates and serve warm.