Broccoli, Cheddar and Mushroom Quiche

adapted by There's Always Thyme to Cook

Custard Filling:
3 eggs
1/4 teaspoon freshly grated nutmeg
1/2 teaspoon salt
1/2 teaspoon freshly ground white pepper
1 cup heavy cream
1/2 cup milk

1 (9-inch) unbaked pie shell

1 1/2 cups broccoli, florets, chopped small
1-1/2 cups sharp cheddar cheese (shredded)
8 ounces mushrooms, white button, sliced
1 shallot, chopped fine
olive oil and a little butter

Preheat oven to 375°. Line pie shell with parchment paper or aluminum foil and fill it with uncooked beans, rice, aluminum or ceramic pie weights. Bake until golden brown and dry. Carefully remove foil and weights. Transfer to a wire rack to cool while making filling.
Heat oil in a large nonstick skillet over high heat. Add shallots, and cook, stirring, until translucent but not brown, about 1 minute. Add mushrooms, and season with salt and pepper. Add broccoli and cook, stirring frequently, until mushrooms first release their liquid and then liquid evaporates and mushrooms are dark golden brown and the broccoli is tender.
Transfer quiche pan to a baking sheet. Sprinkle half the cheese evenly over the bottom of the crust. In a medium bowl, whisk together milk, cream, eggs. Season with nutmeg, salt, and pepper. Mix in the mushrooms, shallots, broccoli and remaining cheese. Pour into the pie shell. Transfer to oven, and bake until just set in the center, about 30 to 35 minutes. Cool on a wire rack for about 10 minutes before slicing.