For the filling, melt the butter in a large pan with a cover. Add apples and sprinkle with the sugar and cinnamon. Cover pan and cook over medium heat for 5 minutes, until apples have exuded juices. Uncover and continue cooking, stirring occasionally, until apples are tender. About a third will have disintegrated, and the rest of the apple slices should remain intact. Cool the filling. May be made several days in advance and stored, covered, in the refrigerator.
To form the pie, preheat the oven to 375 degrees and set a rack in the lowest level. Roll dough to about a 16-inch diameter and center on pan. Spoon filling into center of disk of dough and fold overhanging dough in toward center of pie. Brush the top of the folded-over dough with the egg wash and sprinkle with the sugar.
Bake the pie about 40 minutes, until the dough is a deep golden color and the filling is bubbling. Cool slightly before serving. Or cool completely and reheat before serving