Fit 1 pie crust to bottom and up side of 9 inch deep dish pie plate. Pick bottom of crust with fork and refrigerate while preparing filling.
In a small bowl, blend 1/2 cup of the granulated sugar, the light brown sugar, cornstarch, cinnamon, salt and cloves. Set aside.
Cut apples into 1/2" pieces. Melt butter over medium heat. Add apples, lemon juice and sugar mixture. Cook about 10 minutes until juices thicken. Cool on a rack for 25 minutes.
Pour cooled mixture into the prepared crust lined pie plate. Roll second crust to about 12 inches. Cut 1 inch vent hole in center of dough. Transfer dough to top of pie. Crimp edges together and flute decoratively.
Brush pie with egg mixture.
Sprinkle with remaining 1 teaspoon of sugar. Bake at 400°F for 20 minutes, then reduce temperature to 350°F and bake an additional 25 minutes. Cover pie with foil if it bakes too quickly. Cool at least 1 hour before slicing and serving.