Pre-heat oven to 400 degrees F.
Lay the pie crust over the dish and press the dough down to fit. Trim the edges or tuck them under, and crimp the dough to create a crust.
In a large mixing bowl, cream together the sour cream, granulated sugar, and the egg.
Add in the flour, salt, ground cinnamon, nutmeg, and allspice. Mix until well combined.
Add the vanilla and mix until combined.
Fold in the thinly sliced apples until all the apple slices are evenly distributed.
Pour the filling into the prepared pie crust. Make sure that the apple slices are lying flat, and not sticking up.
While the pie is baking, combine the melted butter, sugar, flour, and cinnamon for the crumb topping in a medium sized mixing bowl. Mix with a fork until a sand-like consistency with pea sized crumbles forms.
Remove the pie from the oven. Add the crumb topping mixture evenly over top of the pie. Return the pie to the oven and bake for an additional 20 minutes.
Place the cooked pie onto a wire rack to cool for 1 hour before serving.