To make the crust, combine all of the ingredients in a small bowl and blend with a fork, pastry cutter or your fingers until well blended - it will look like big, soft crumbs. Press into the bottom and about an inch up the sides of a buttered or sprayed springform pan.
To make the filling, beat the cream cheese and sugar until smooth and lump-free; add the eggs, one at a time, then the reserved egg white and vanilla. Pour into the pastry lined pan. Preheat the oven to 400F.
Thinly slice the apple(s) and toss with sugar and cinnamon to coat; scatter over the top of the cheesecake. Bake for 12 minutes, then reduce the heat to 375F and bake for another 30-35 minutes, until puffed and golden but slightly jiggly - it will firm up as it cools. Let cool in the pan, then refrigerate for a few hours, or overnight.