Blend flour and salt in processor. Add butter; process until coarse meal forms. Add ice water; process until moist clumps form. Gather dough into ball; flatten into disk. Wrap in plastic and chill 30 minutes. (Can be made 1 day ahead. Keep chilled. Soften slightly before rolling out.)
Preheat oven to 375°F. Roll out dough on floured surface to 15-inch round. Transfer to 9-inch-diameter tart pan with removable bottom. Trim off excess dough. Freeze crust 20 minutes.
Line crust with foil. Fill with dried beans or pie weights. Bake until sides are set, about 20 minutes. Remove foil and beans; bake until pale golden, piercing with toothpick if crust bubbles, about 15 minutes. Cool. Maintain oven temperature.
Bring cream and garlic to boil in heavy medium saucepan. Reduce heat to medium; simmer until mixture is reduced to 1 cup, whisking occasionally, about 15 minutes. Cool. Puree in processor. Blend in egg and salt.
Meanwhile, heat oil in large skillet over medium-high heat. Add mushrooms; sauté until tender, about 5 minutes. Season with salt and pepper. Cool.
Spread goat cheese over bottom of crust. Sprinkle mushrooms over. Spoon cream mixture over. Bake until filling is set, about 20 minutes. Cool on rack.
Bon Appétit, November 1997