Make the crust: Pulse the flour and salt in a food processor to combine. Add 2 tablespoons butter; pulse a few times until the mixture looks like cornmeal. Add the remaining 4 tablespoons butter and pulse until it is in pea-size pieces. Add the cream cheese; pulse a few more times until the dough just comes together. Add the vinegar and 1 tablespoon ice water; pulse a few times until the dough is moist. Divide the dough between two pieces of plastic wrap. Shape each into a disk and wrap. Refrigerate until firm, at least 1 hour or overnight.
Put a baking sheet on the middle oven rack and preheat to 425 degrees F for 30 minutes. Meanwhile, make the filling: Peel the apples and slice about 1/4 inch thick; toss with the berries, granulated sugar, flour, vanilla, butter and salt in a large bowl. Set aside.
Roll out 1 disk of dough into a 12-inch round on a lightly floured surface. Ease into a 9-inch pie plate. Fold the overhanging dough under itself. Add the filling. Roll out the remaining disk of dough into an 8-inch round on a lightly floured surface; slice into 12 strips. Brush the strips with some of the beaten egg. One at a time, twist the strips of dough and, working from the center of the pie outward, arrange the strips on the pie to make one continuous coil.
Brush the top of the pie with the remaining beaten egg and sprinkle with the turbinado sugar. Transfer the pie to the hot baking sheet in the oven and bake 15 minutes. Reduce the oven temperature to 350 degrees F and continue baking until the crust is golden and the filling is bubbling, 50 to 55 more minutes. (Tent with foil if the crust browns too quickly.) Transfer to a rack and let cool completely.