Step 1Melt the butter in a large saucepan over medium-low heat. Add the apples and stir gently to coat the apples evenly with the melted butter. Sprinkle the apples with the sugar and cook until the apples become semi-translucent, but still hold their shape, 10 to 12 minutes, stirring occasionally. If too much liquid remains in the pan, remove the apples and continue cooking the liquid until it has reduced to a syrup. Return the apples to the pan and let cool completely.
Step 1Place the flour and salt in the middle of a flat surface. Make a well in the flour mixture. Put the butter in the well. With a pastry cutter, cut the butter into the flour mixture. Scoop the loose flour from the sides and quickly work it into the butter. Continue this process until the mixture becomes large pea-size lumps. This should take about a minute. Sprinkle 4 tablespoons of chilled water over the flour mixture. Using your fingertips, pat and press the dough together into a ball. If the dough is still dry and loose, add an additional tablespoon or two of chilled water. Continue patting and pressing the dough until you can mold it into a disk, about 6 inches in diameter. Divide the dough in half, form each half into a disk and wrap with plastic. Refrigerate at least 1 hour.
Step 2Once the dough has chilled, lightly flour a flat surface and a rolling pin. Take 1 disk of dough out of the refrigerator to make the bottom crust. Beginning from the center of the disk, roll out the dough to the edges to make a circle, slightly larger than a 9-inch pie pan and about 1/8-inch thick. Roll only in one direction. Keep rotating the circle as you roll, so it doesn't stick to the flat surface. Fold the dough in half and transfer it to a 9-inch pie pan. Unfold the circle and press it into the pan with your fingers and allow the dough to hang over the pie pan. Chill the pan in the refrigerator while you roll out the top dough.
Step 3For the top dough, repeat the same rolling process.
Step 1Heat the oven to 350 degrees.
Step 2Pour the apple filling into the bottom crust, spreading evenly in the pan. Roll the top dough around the rolling pin and then unroll it over the filling, pressing the top and bottom crusts together to seal. Use a wet fork to crimp the rim of the pie. Use the tines of a fork to poke some holes in the top crust for ventilation.
Step 3Beat the egg yolk and milk and brush over the top of the pie to make a shiny glazed finish. Set the pie pan on a baking sheet and bake until the top crust is golden, about 65 to 70 minutes. Let the pie cool a little before serving.