Combine the apples and water in the saucepan and bring to a boil. Turn off the heat and let sit, covered, for 30 minutes. Drain in the colander and turn into a mixing bowl. Sprinkle with the cinnamon, sugar, and salt and beat well. Separate one of the eggs and reserve the white for the glaze. Add that yolk and the three whole eggs to the apple mixture along with the butter and beat well again.
Preheat oven to 350°F (177°C).
Prepare the pan by greasing it lightly with butter. Roll out one-half of the dough (8 ounces or 225 g) on a lightly floured surface to an 11-inch (27½ cm) diameter. Fit it into the pan and add the filling. Roll out the other half of the dough and drape it over the top of the pie. Dampen the edges and crimp the two crusts together, sealing well. Beat the reserved egg white with 1 tablespoon water. Brush the top of the dough well with the egg white and sprinkle the 1 tablespoon sugar over the surface. Cut 8 to 12 small slits in the top crust so steam can escape as the pie bakes. Bake in the middle level of the preheated oven for about 1 hour or until the crust is golden brown. Serve hot with whipped cream. This pie reheats well.