1/2  cup butter
 1/3  cup sugar
 1/4  tsp  vanilla
 1    cup  flour
 8 oz pkg cream cheese
 1/2 tsp vanilla
 1/2 cup sugar
 1 egg, beaten
 4 cups diced apples (approx. 8 apples)
 1/3 cup sugar
 Chopped nuts
 
 Preheat oven to 450 degrees F.  Cream first 4 ingredients together.  Spread in
 bottom on greased springform pan and approx. 1 1/2 inches up side.  Blend
 next 3 ingredients until smooth.  Pour on top on dough.  Mix remaining 
 ingredients together, except nuts.  Place over cream cheese mixture.  Sprinkle
 chopped nuts on top. Bake for 10 minutes.  Lower heat to 400 degrees F and
 bake for 25 minutes.  Do not remove ring until cake has set overnight and is
 well together.  Run knife around side of springform pan while cake is cooling.
 so it is not too stuck to side.
 Note:  Alternative to chopped nuts might be brown sugar and cinnamon mixture
 or a topping similar to that on an apple crisp recipe with oatmeal.