Preheat the oven to 450 degrees F (230 degrees C).

Mix flour, butter, 1/3 cup sugar, and 1/4 teaspoon vanilla extract together in a medium bowl. Press crust into bottom of a 9-inch springform pan. Set aside.

Blend cream cheese, 1/4 cup sugar, egg, and 1/2 teaspoon vanilla extract together in a large bowl until well combined. Pour filling over crust.

Mix apples, 1/3 cup sugar, and cinnamon together in a large bowl; spread over filling.

Bake in the preheated oven for 10 minutes. Reduce heat to 400 degrees F (200 degrees C); continue baking for 25 minutes. Sprinkle almonds over torte; continue baking until apples are tender and almonds are golden. Cool; remove from pan.