Lightly prick bottom of shell all over with a fork, then line with foil and fill with pie weights. Bake until side is set and edge is pale golden, 18 to 20 minutes. Carefully remove foil and weights and bake shell until bottom is golden, 10 to 15 minutes more.
04Cool completely in pan on a rack, about 15 minutes.
05Heat butter and oil in a 12-inch heavy skillet over moderately high heat until foam subsides, then sauté mushrooms, shallot, thyme, 1/2 teaspoon salt, and 1/4 teaspoon pepper, stirring frequently, until mushrooms are tender and any liquid given off is evaporated, 8 to 10 minutes. Transfer to a bowl and cool to room temperature.
06Whisk together crème fraîche, heavy cream, whole egg, yolk, and remaining 1/4 teaspoon salt and 1/8 teaspoon pepper in a medium bowl until combined.
07Reduce oven temperature to 325°F.
08Scatter mushrooms evenly in tart shell and pour custard over them. Bake tart in pan on a baking sheet until custard is just set and slightly puffed, 35 to 45 minutes.
09Cool tart in pan on rack at least 20 minutes, then remove side of pan. Serve tart warm or at room temperature.
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Not rich — missing servings, total time, or calories.