For streusel topping: Mix in large mixing bowl sugars, butter, cinnamon, and vanilla. Add flour. The mixture should not come together but be crumbling. Adjust flour accordingly.

For torte: mix butter and sugar in large mixing bowl. Add eggs, rum, and mix well. In small mixing bowl combine flour, baking powder and cornstarch. Add dry ingredients to large bowl and mix well. Add milk. Put in 10 inch baking pan. Place apples on top. Sprinkle streusel topping over apples. Bake 35 to 40 minutes in 350 ° oven.