Melt butter in a large nonstick skillet over moderate heat. Add apples (fresh and dried), cranberries, cinnamon, nutmeg, and salt; cook, stirring occasionally, until apples are softened, about 8 minutes. Add sugar and cook, stirring, until dissolved, about 2 minutes more. Remove pan from heat; stir in flour and juice. Let cool.

Meanwhile, preheat oven to 350 degree F and arrange rack in lower third of oven. Roll out 1 piece of dough according to Piecrust directions, for bottom crust, trimming overhang to 1/4 inch.

Roll out remaining piece of dough into a 17-inch round. Trim into a 13-inch round and transfer to a lightly floured cookie sheet. Decoratively cut out circles with a 1/4- or 1/3-inch plain pastry tip dipped in flour and a larger circle (about 1 inch) in center. Chill until firm, about 15 minutes.

Spoon filling into bottom crust. Cover with top crust and trim overhang to 1/2 inch; tuck under bottom crust, pressing edges together to seal. Brush crust with egg and chill pie until dough is firm, about 15 minutes.

Bake pie until golden brown and apples are tender, about 45 minutes. Transfer to rack and cool 30 minutes before cutting and serving. Makes 8 servings.