Roll out the dough on a lightly floured surface to a large circle about 1/8-inch thick. Fit it, without stretching, into a buttered 8- to 9-inch pie pan. Trim off the excess dough, leaving a 3/4-inch border. Fold under the edge of dough, pressing along rim of the pan and forming a high, fluted border.
Chill the pie shell while you preheat the oven to 375° , with a rack in the lower third.
In a bowl, whisk together the boiled cider, sugar, melted butter, lemon juice, salt, and eggs. Add the grated apples and stir to blend well. Pour the filing into the pie shell; sprinkle the brown sugar and nutmeg over the top.
Bake until mixture is just set in the center, usually 50 minutes.
Let the pie cool on a wire rack. Serve warm, topped with ice cream or whipped cream.<