Mix crumbs and 1/2 tsp cinnamon. Stir in butter and when well mixed, press firmly onto bottom and up side of 9 inch pie plate.
Use an 8 slice apple slicer/corer on the peeled apple. Slice some of the wedges into 3 or 4 slices so that you have 16 to 18 thin slices. Chop the remainder of the wedges into small pieces. Set slices and chopped apple aside.
Beat cream cheese, 1/2 cup of sugar, 1/2 tsp cinnamon and vanilla in a large bowl with electric mixer on medium speed until well blended. Add eggs, one at a time, beating just until well blended after each addition. Fold in chopped apples and pour mixture into crust.
Arrange apple slices in a circle on the top of the pie putting 2 slices in the middle. Mix 3 Tbsp of sugar and 1/4 tsp of cinnamon together and sprinkle evenly over pie.
Bake for 40 minutes or until center is almost set. Cool on a wire rack. Refrigerate 3 hours or overnight. Store leftover cheesecake in refrigerator.