Step 1: Make the crust. In a large bowl, whisk together flour and salt. Add cold cubed butter and use a pastry cutter or fork to cut it into the flour until pea-sized crumbs form.
Step 2: Gradually add ice water, 1 tablespoon at a time, mixing until the dough just comes together. Divide into two disks, wrap in plastic, and refrigerate for at least 30 minutes.
Step 3: Preheat oven to 375°F (190°C). In a large bowl, combine sliced apples, sugar, flour, cinnamon, nutmeg, and lemon juice. Toss to coat evenly.
Step 4: Roll out one dough disk on a floured surface to fit a 9-inch pie dish. Place in dish and trim edges. Add apple filling and dot with cubed butter.
Step 5: Roll out the second dough disk and place over filling. Crimp edges to seal, then cut slits in the top for venting. Brush with beaten egg and sprinkle with coarse sugar if using.
Step 6: Bake for 45-50 minutes, until crust is golden brown and filling is bubbly. Cool on a wire rack before serving.