For the crust: Put the flour and salt in a large bowl. Work in the butter and shortening with a pastry cutter until it resembles tiny pebbles. Add the egg. Stir in the water and vinegar until just combined, adding a little more flour if the dough is too wet or a little more water if it’s too crumbly. Divide the dough in half; flatten into disks. Wrap in plastic wrap and chill for 30 minutes. For the filling: Melt 4 tablespoons butter in a large nonstick skillet over medium heat. Add the apples and lemon juice, then sprinkle in the sugars and cook, tossing, until the apples start softening, 5 minutes. Increase the heat to get the juices bubbling; cook until glazed, about 1 minute. Sprinkle in the flour, cinnamon and salt. Simmer just until the filling thickens, about 1 minute. Remove to a bowl and let cool. Roll out the dough on a floured surface into a 13-inch round. Place in a 9-inch pie plate. Add the apple filling and dot with the remaining 2 tablespoons butter. Roll out the remaining disk of dough on a floured surface into a 13-inch round. Lay the dough over the filling and fold the overhanging dough under itself; crimp the edges and cut a few small slits in the top crust. Chill for 30 minutes. Place a baking sheet on the bottom oven rack; preheat to 450 ̊. Combine the coarse sugar, cinnamon and chile powder. Brush the pie with cream; sprinkle with the spiced sugar. Put the pie on the hot baking sheet and reduce the oven temperature to 375 ̊. Bake until the crust is golden and the filling is bubbly, 1 hour. (If the crust is browning too quickly, cover loosely with foil.) Transfer to a rack and let cool.