1. Heat oven to 450 degrees F.
2. For bottom crust, roll out half of pastry on well-floured board into 12-inch circle, 1/8 inch thick. Brush off any excess flour. Transfer to 8-inch pie pan. Refrigerate while preparing filling.
3. Combine sugar, cornstarch, cinnamon, nutmeg and cloves in small bowl.
4. Keeping McIntosh apples separate, peel, core and slice apples 1/8 inch thick. Place McIntosh in one bowl, the remaining apples in a second bowl. Drizzle lemon juice over both bowls of apples.
5. Toss McIntosh apples in 1/4 cup of sugar mixture; set aside. Toss Granny Smith and Golden Delicious apples with remaining sugar mixture.
6. Melt butter in large skillet. Scrape Golden DeliciousGranny Smith mixture into skillet; saute for 10 minutes or until softened. Cool to room temperature.
7. Once the sauteed apples are cooled, add McIntosh apples. Arrange apple mixture in dough-lined pan, packing apples as tightly as possible. Brush edge of dough with beaten egg.
8. For top crust, roll out remaining dough on well-floured surface to a 11-inch circle. Cut out 1-inch circle in center of dough. Center dough over apple mixture. Trim dough with 1/4-inch overhang. Crimp edges together. Brush top crust with beaten egg.
9. Bake on bottom rack in 450 degrees F oven 10 minutes. Reduce heat to 350 degrees F. Bake 45 to 55 minutes. If crust begins to brown too quickly, cover loosely with foil for last 10 minutes of baking. Cool pie on wire rack to room temperature, or reheat briefly to serve warm.Double-Crust Pie Pastry:
10. Stir together flour and salt in medium-size bowl. Cut in butter and shortening with a pastry blender until the mixture resembles coarse meal. Sprinkle cold water, 1 tablespoon at a time, over mixture, tossing lightly with fork after each addition until pastry is just moist enough to hold together. Divide pastry in half; shape each half into a dish. Wrap in plastic wrap. Chill for 1 hour or up to 2 days.