Step 1

In a food processor, pulse the flour with the butter and salt until the mixture resembles coarse meal. Add the water and pulse a few times until a crumbly dough forms. Turn the dough out onto a work surface and knead 3 times, until it just comes together. Pat into a disk, wrap in plastic and refrigerate for at least 1 hour.

Step 2

Preheat the oven to 350°. On a lightly floured work surface, roll the dough out to a 12-inch round. Fit the round into a 10 1/2-inch tart pan with a removable bottom. Roll the rolling pin across the top of the pan to remove the excess dough. Line the dough with foil and fill it with rice or pie weights. Bake the tart shell for about 1 hour, or until golden around the edge. Remove the foil and rice and bake the shell for about 18 minutes longer, or until golden on the bottom. Transfer the tart shell to a wire rack and let it cool completely. Increase the oven temperature to 375°.

Step 3

In a large skillet, melt the butter. Add the mushrooms, season with salt and pepper and cook over moderate heat, stirring occasionally, until tender and browned, about 8 minutes. Let cool.

Step 4

In a medium bowl, whisk the eggs with the cream, milk, 3/4 teaspoon of salt and 1/4 teaspoon of pepper. Scatter the mushrooms, ham and cheese in the tart shell and pour the custard on top. Bake the quiche for about 30 minutes, or until  it is lightly browned on top and the custard is just set. Transfer to a rack to cool for 15 to 20 minutes. Unmold the quiche, cut into wedges and serve.