Lightly oil a 9-inch springform pan. Place on a rimmed baking sheet lined with parchment.

Roll pâte brisée to a 16-inch circle. Roll up on rolling pin and transfer to springform pan.Carefully press into place, leaving dough overhanging the edge. Trim overhanging edge to an inch, reserving excess dough, and press into the sides. Refrigerate 20 minutes.

Preheat oven to 375°F.

Line interior of crust with parchment and place several cups of rice inside to hold down crust and parchment.

Bake 40 minutes, or until edges of crust are golden. Remove rice and parchment and bake an additional 15 minutes, or until bottom of crust is golden brown. Remove and let cool.

If possible, carefully patch any cracks in the crust with reserved dough.

Heat oil in a large skillet over high heat. Add mushrooms, season with salt and pepper, and cook on high, stirring often, until they start to become tender, about 5 minutes.

Add butter, leeks, and thyme, reduce heat to medium and cook until mushrooms are completely tender, about 12 minutes. Remove from heat and let cool.

Preheat oven to 325°F.

Place about 1/3 of the cheese on the bottom of the crust, followed by half the mushrooms.

In the bowl of a mixer fitted with the whisk attachment, beat on high until frothy 3 eggs, 1 cup milk, 1 cup cream, 1 tsp kosher salt, 1/8 tsp pepper, and a pinch of nutmeg, about 1 minute.

Pour custard over mushrooms.

Repeat a layer of cheese, and the remaining mushrooms. Again, make half the custard as before and pour over mushrooms. Top with remaining cheese.

Bake for about 90 minutes, until the custard is set. You can check if it's done by inserting an instant read thermometer into the center. It should read between 165° and 185°F. Alternatively, insert a sharp knife in the center. If the knife comes out clean, the quiche is done.

Remove from oven, and, using a sharp serrated knife, trim crust so it's level with the top of the pan.

Slice and serve.