1. Make tart shell: In food processor, pulse flour with butter and salt until course meal texture. Add water and pulse a few times until crumbly dough forms. Turn out dough onto lightly floured surface and knead three times. Pat dough into a disk, wrap in plastic wrap and refrigerate for 1 hour.
2. Preheat oven to 350 F. Roll out dough to a 12″ round. Fit dough into a 10 1/2″ tart pan (with removable bottom). Roll pin across the top to remove excess dough. Line dough with foil and fill with rice or pie weights. Bake for 1 hour or until golden brown around the edges. Remove foil and rice and bake for about 18 minutes longer. Transfer to wire rack and cool completely. Increase oven temperature to 375 F.
3. Filling: In large skillet, melt butter. Add mushrooms, season with salt and pepper. Cook over medium heat until mushrooms are tender and browned.
4. In medium bowl, whisk eggs with cream and milk, add 3/4 tsp salt and 1/4 tsp pepper. Scatter the mushrooms, ham and cheese in tart shell and pour custard on top. Bake for about 30 minutes or until lightly browned on top and custard is set. Cool for 15-20 minutes. Unmold, cut and serve.