Cream together butter, 1/3 cup sugar, vanilla, and flour. Press crust mixture into the flat bottom of a 9-inch springform pan. Set aside.
In a medium bowl, blend cream cheese and 1/4 cup sugar. Beat in egg and vanilla. Pour cheese mixture over crust.
Combine 1/3 cup sugar and 1/2 teaspoon cinnamon. Toss the sliced apples with the sugar mixture and spread over the cheese filling.
Bake for 10 minutes. Reduce heat to 400 degrees F (200 degrees C) and continue baking for 25 minutes. Sprinkle almonds over top of torte. Continue baking until almonds are lightly browned and apples are tender. Cool before removing from pan.