Sift the pastry flour and salt into a large bowl. Cut the shortening and cold butter cubes into the flour mixture using a pastry cutter or your fingers until the mixture resembles coarse crumbs. In a cup, whisk together the ice cold water and white vinegar, then pour it into the flour mixture. Gently mix until the dough just comes together and is easy to handle. Try not to overwork the dough, as this will help keep it tender.
Divide the dough into two pieces. On a lightly floured counter, roll out one piece into a rectangle about as thick as typical pie dough. Spread a light coating of salted butter over the surface, then generously sprinkle with ground cinnamon and granulated sugar. Starting at the long edge, roll up the dough tightly jelly roll style. Using a sharp knife or pastry cutter, slice the roll into 1/4 to 1/2 inch thick rounds. Press the rounds, flat side down, into the bottom and up the sides of a 9-inch pie plate, overlapping and sealing as needed. Repeat this process with the second half of dough and set these slices aside for the top crust.
Peel, core, and slice the apples thinly. Place them in a large saucepan and sprinkle with all-purpose flour, granulated sugar, ground cinnamon, freshly grated nutmeg, and the juice of half a lemon. Cook the apples over medium-low heat, stirring occasionally, until they start to soften, about 10-15 minutes. I like cooking the apples a bit before baking because it gives the filling a really rich flavor and ensures the apples are perfectly tender.
Pour the warm apple mixture from Step 3 into the prepared pie plate lined with cinnamon roll crust from Step 2. Press down lightly on the apples to help them lay flat and minimize air pockets, making a nice, thick pie. Dot the top of the apples evenly with salted butter.
Arrange the remaining cinnamon roll slices from Step 2 over the apple filling, covering the top in a decorative pattern. Brush the top crust with milk to help it turn golden and glossy, then sprinkle coarse sugar evenly over the pie for texture and shine. I love using coarse sugar here as it gives the pie a beautiful finish and a pleasant crunch.
Place the pie in a preheated 425ºF oven and bake for about 40 minutes or until the crust is golden brown and the apples are soft. If you notice the crust browning too quickly, cover the edges with foil to prevent over-browning. Let the pie cool slightly before slicing and serving.