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.