Preheat oven to 400 F. On lightly floured surface roll dough to a 14-inch round. Transfer to an 11-inch tart pan with removable bottom. Trim edges; prick bottom with tines of fork.
Line pastry shell with foil and and pastry weights, dried beans, or raw rice. Bake 15 minutes. Remove foil and weights.
Bake 5 to 6 minutes longer or just until pastry starts to turn golden. Brush with egg white; bake 1 minute longer. Cool completely on wire rack.
In large skillet, melt butter over medium-low heat. Add mushrooms, garlic, oregano, and pepper. Saute until mushrooms are golden and liquid has evaporated, about 8 minutes; cool to room temperature.
Cover bottom of tart shell with mozzarella, cutting slices to fill in spaces. Top with mushroom mixture then sprinkle with asiago and walnuts. Bake 20 minutes.
Cool 5 minutes on wire rack before removing outer ring. Serve warm.
Makes 8 servings.