In a Dutch oven combine the 3/4 cup water and the 3 tablespoons sugar. Bring to boiling over medium-high heat; add the apples and the cranberries. Cover and cook for 4 minutes, stirring once. Drain well in a colander.
In a large mixing bowl combine the 3/4 cup sugar, the flour, nutmeg, and rum or apple juice concentrate. Add apple mixture; toss gently to combine. Set mixture aside while preparing the pastry. Move oven rack to lowest setting. Preheat oven to 375 degrees F.
Prepare Pastry for Double Crust Pie (below). On a lightly floured surface roll half of the dough into a 12-inch circle. Wrap the pastry around rolling pin; unroll onto a 9-inch pie plate. Ease pastry into pie plate, being careful not to stretch pastry.
Stir fruit filling to distribute spices, flour, and sugar evenly. Spoon into the pastry-lined pie plate. Trim pastry to edge of pie plate. On a lightly floured surface roll remaining dough into a 12-inch circle. Cut slits for steam to escape. Place on top of fruit filling. Trim top crust to 1/2 inch beyond edge of pie plate. Fold top pastry under bottom pastry. Crimp edge as desired. Brush top with a mixture of beaten egg and 1 tablespoon water. To prevent overbrowning, cover the edge of pie with foil.
Place pie on a cookie sheet to catch any drips. Bake 30 minutes. Remove foil. Bake for 35 to 40 minutes more or until the top is golden. Cool on a wire rack.
In a medium skillet melt margarine or butter. Add broken pecans. Cook and stir over medium-low heat for 3 to 5 minutes or until the pecans are lightly toasted. Carefully add corn syrup, brown sugar, and 2 tablespoons water (mixture may splatter when the syrup comes in contact with the hot pan). Cook and stir with wooden spoon until bubbly and the brown sugar is dissolved. Add whipping cream. Bring mixture to boiling; reduce heat. Boil gently, uncovered, over low heat for 5 minutes. Allow to cool slightly. Serve pie slightly warm or at room temperature with warm sauce. Makes 8 servings.
Pastry for a Double-Crust Pie
In a bowl stir together flour and salt. Using a pastry blender, cut in shortening until pieces are pea size. Sprinkle 1 tablespoon cold water over part of the mixture; gently toss with a fork. Push moistened dough to side of bowl. Repeat using 1 tablespoon cold water at a time until all the dough is moistened (6 to 7 tablespoons total). Divide dough in half. Form each half into a ball. On a lightly floured surface, flatten 1 dough ball. Roll from center to edges into a 12-inch circle. To transfer pastry, wrap it around the rolling pin; unroll into a 9-inch pie plate. Ease pastry into pie plate, being careful not to stretch pastry. Fill as above. roll remaining dough into a circle about 12 inches in diameter. Continue as above.