For the dough:
Add the flour, salt and sugar to the bowl of a food processor and process for a few seconds to combine. Add the butter and process until the mixture resembles coarse meal, about 10 seconds. With the food processor running, slowly add the ice water until the dough holds together, about 10-15 seconds at most.
Empty the dough onto a lightly floured work surface. Divide into two. Place each half on a sheet of plastic wrap, flatten and form two discs. Wrap and refrigerate for 1 hour and up to 24 hours before using.
For the pies:
Heat oven to 375 degrees. Line a baking sheet with parchment paper. On a lightly floured surface, roll out the dough into two 1/8 inch-thick circles. Using a lightly floured pastry circle (I used a 4-inch circle), cut out about 16 circles. Arrange 8 of the circles on the parchment and set the rest aside in a single layer on the floured work surface.
In a large bowl, combine the apples, granulated sugar, lemon zest and juice, cinnamon and flour and toss well to combine. Spoon a small amount of the apples (about 4 apple slices per 4-inch round) onto the dough rounds that rest on the parchment lined baking sheet. Cover with the remaining pastry circles. Cut small steam vents across the top of each hand pie. Seal by carefully crimping the edges of each pie. Brush the top and edges of each pie with the beaten egg and sprinkle with a generous amount of turbinado sugar. Bake until the tops and edges are golden, about 25 minutes. Let cool on a wire rack before serving.