Preheat the oven to 375 degrees F.

In a bowl, mix together the crumbs, sugar, and cinnamon. Add the butter and mix well. Using the back of a spoon, press evenly into the bottom and slightly up the sides of a 9-inch springform pan. Bake until golden, about 8 minutes. Remove from the oven and cool before filling.

In a large bowl, beat the cream cheese with the paddle attachment of an electric mixer, or with a large, heavy wooden spoon until creamy and smooth. Add the sugar a few tablespoons at a time, and when well incorporated, add the flour, lemon peel, orange peel, and vanilla extract. Add the eggs and heavy cream, beating on low speed just until combined, scraping down the sides of the bowl to incorporate all the ingredients.

Pour the batter into the prepared pan and bake in the middle of the oven until set, but the center is still slightly soft (but not wobbly), about 55 minutes to 1 hour and 10 minutes. Remove from the oven, loosen the outer ring, and let cool in the pan on a wire rack. Refrigerate the cake, loosely covered, for 6 hours or overnight.

Remove the cake from the refrigerator and bring to room temperature.

To make the topping, in a heavy, medium saucepan, combine the 1/2 cup sugar and water, and bring to a boil. Lower the heat and cook, stirring occasionally, until the sugar is dissolved. Continue cooking until amber in color, 7 to 10 minutes, swirling the pan occasionally. Add the butter, stir, and cook over low heat until the butter is melted and evenly incorporated. Add the apples and stir to coat with the caramel. Cook, stirring, over medium heat until the apples are tender, about 5 minutes. Remove from the heat and cool before topping the cheesecake.

Top the cheesecake with the caramelized apple topping and serve.