Preheat oven to 450 degrees. Unroll crust completely and dust bottom side with 1 TBSP flour. Press firmly onto bottom and up sides of 9-inch-diameter pie pan- flute edges. Pierce with fork several times and cover edges with foil to keep from browning too fast. Bake until light golden brown about 15 to 17 minutes. Reduce oven temperature to 325°F.
While crust is baking, melt butter in heavy large skillet over medium-high heat. Add chopped shallots and sauté until they begin to soften, approx 2 minutes. Add mushrooms; sprinkle with salt and pepper and sauté until mushrooms are tender and beginning to brown, approx 8- 10 minutes. Remove from heat and let cool.
Whisk eggs, milk, half and half, salt, pepper, and nutmeg in large bowl. Stir in 1 cup Fontina cheese and cooled sautéed mushrooms. Pour filling into crust. Sprinkle with remaining 1/2 cup fontina.
Bake until golden brown, and just set in center, approx 45 minutes. Cool 30 minutes. Cut into wedges and serve.