In a large mixing bowl, stir together the 3/4 cup sugar and 3 tablespoons flour. Add the sour cream, egg, vanilla, and salt. Stir together well.
Add the apple slices. Gently toss them until coated. Transfer the apple mixture to the unbaked piecrust. Bake in a 350 degree F oven for about 30 minutes.
In a medium mixing bowl, stir together the 1/3 cup sugar, 1/3 cup flour, and cinnamon. Using a pastry blender, cut in butter until mixture resembles coarse crumbs.
Sprinkle the crumb topping over the hot filling. Bake the pie for 35 minutes more or until the pastry edges are golden. Cool the pie on a wire rack for 1 hour. Cover and refrigerate the pie to store.