Preheat oven to 450°F. In a medium bowl toss together hash browns, butter and 1/4 teaspoon of the salt. Transfer hash brown mixture to a 9-inch pie plate, pressing into the bottom and up the sides to form a crust. Bake for 20 to 25 minutes or until golden brown and starting to crisp. Reduce oven temperature to 350°F.
Meanwhile, in a large skillet cook bacon until crisp. Drain, reserving 1 tablespoon of the drippings. Crumble bacon; set aside. Cook mushrooms and shallot in the reserved drippings over medium heat for 3 to 5 minutes or until tender but not brown. Cool slightly.
In a large bowl combine eggs, half-and-half, green onions, thyme, nutmeg and remaining 1/4 teaspoon salt. Stir in mushroom mixture and bacon. In a small bowl toss together cheese and flour. Add to egg mixture; mix well.
Pour egg mixture into hash-brown-lined pie pan. Bake for 30 to 35 minutes or until a knife inserted near the center comes out clean. Let stand for 10 minutes before serving.