Make the crust: Cream the butter and sugar. Stir in the vanilla. Finally, mix in the flour to make a smooth dough. Alternately, put the butter, sugar, vanilla, and flour in the food processor and pulse to crumbs. Pour them into your pan and press into place. Press into the bottom of an 8-inch springform pan, giving it about a 1-inch rim. Bake 15 minute, or until lightly golden. Remove the tart shell from the oven.
While the crust bakes, beat together the cream cheese, sugar, egg and vanilla for the cream filling until smooth. Make the topping by tossing the apple slices with the cinnamon, sugar, and nuts.
Remove the tart shell from the oven. Spread over the cream mixture. Arrange the apple slices on top, and then scatter over the nuts. Bake until the apples are tender and golden, about 40 minutes.