In a medium bowl, combine flour and brown sugar. Cut in butter with a pastry blender until mixture is crumbly. Press evenly into a 13x9-inch baking pan lined with heavy-duty aluminum foil. Bake 15 minutes, or until lightly browned.
In a large bowl, beat cream cheese with an electric mixer at medium speed until smooth. Beat in 1/2 cup sugar, eggs, and vanilla until smooth. Pour over warm crust.
In a small bowl, stir together chopped apples, 2 tablespoons sugar and cinnamon. Top cheesecake part with chopped apples.
In a small bowl, combine all ingredients and sprinkle evenly over apples.
Bake 30 minutes, or until filling is set (until a knife inserted in the center comes out clean)