How to Make It
In a large bowl, toss together the flour and salt. Using a pastry blender or two knives, cut in the shortening until the mixture is mealy. Sprinkle in 4 tablespoons of the ice water and stir with a fork until the dough comes together. If it is too dry and crumbly, add the remaining 1 tablespoon water, 1 teaspoon at a time.
Halve the dough and pat it into two 7-inch disks. Wrap each disk in wax paper and refrigerate until chilled, about 30 minutes.
Arrange one rack in the bottom third of the oven and another in the middle; preheat the oven to 450°. On a lightly floured surface, roll out 1 disk of dough into a 10- to 11-inch round. Transfer the dough to an 8-inch pie pan. Do not trim the overhanging pastry. Roll out the second disk of dough into an 11- to 12-inch round and transfer it to a parchment-lined baking sheet. Refrigerate the pastry while you proceed.
Toss the apples with the pineapple and lemon juice. In a bowl, mix together the sugar, flour, nutmeg and cinnamon. Toss the dry ingredients with the fruit.
Scrape the filling into the pie shell (it may look like too much filling, but it shrinks as it bakes). Moisten the overhanging edge of pastry with water. Place the top crust over the filling. Trim the edge so it's even, then crimp to seal. Cut a few vents in the top. Brush the pie with the milk and sprinkle the sugar on top.
Bake the pie on the bottom rack of the oven for 20 minutes, then transfer it to the middle rack and bake 40 to 45 minutes longer, until the crust is golden brown and the apples are tender when gently pierced. Transfer to a rack to cool before serving.