How to Make It
Make the pie dough: Combine the flour, salt and sugar in the bowl of a food processor and pulse to combine. Add the butter and pulse until the consistency of coarse meal. Add about ½ cup of water and pulse to combine, adding more water by the tablespoon until dough just holds together when squeezed. Do not overmix. Divide dough into two balls, roughly two-thirds and one-third. Flatten each portion into a disc and wrap in plastic. Refrigerate at least 45 minutes or overnight. Dough can be frozen for up to one month.
Make the filling: Peel and core the apples. Reserve one half of one apple, then quarter the rest. Cut the quarters into four slices and transfer to a large mixing bowl. Toss with raspberries, sugar, cinnamon, cornstarch, and a generous pinch of salt. Set aside to macerate while you roll out the crust.
On a lightly floured work surface, roll the larger portion of dough out to a circle about ⅛-inch thick. Transfer to a 10-inch cast iron skillet (or other oven-safe skillet). Trim edges, leaving a 1-inch overhang. Arrange filling in pie shell. Cut reserved apple half into a triangle to form the nose, place in center of pie. Dot with butter. Fold overhang on top of filling as if making a galette.
Roll remaining pie dough into a 1/8-inch thick square, about 14 inches across. Cut into 1½-inch wide strips using a pizza wheel or sharp knife. Brush the folded edge of the bottom crust with egg wash, then lay strips of remaining dough over the top of the pie to form the mummy wrapping. Tuck overhanging edges between crust and sides of skillet. Refrigerate assembled pie at least 45 minutes.
Preheat oven to 450°F. Brush top of pie with egg wash and sprinkle with turbinado sugar. Place the skillet on a parchment-lined sheet pan to catch any drips and transfer to preheated oven. Immediately lower oven temperature to 375°F. Bake until top is deep golden brown and filling is bubbly, about 90 minutes, rotating halfway through (tent with aluminum foil if crust gets too dark.) Transfer to wire rack to cool.