In a medium bowl, stir together graham cracker crumbs, sugar and butter. Dump mixture into a 9" springform pan, and use the bottom of a dry measuring cup to press it evenly into the bottom and about 1" up the sides. Bake for 10 minutes, then remove from the oven and place inside a large baking dish.

Meanwhile, in a stand mixer, beat the cream cheese and mascarpone with the sugar on medium speed until well combined, about a minute. Beat in the eggs, one at a time, and then the cinnamon. Scrape into the baked crust.

Make a water bath for the cake by pouring boiling water into the large baking dish until it comes an inch up the side of the springform pan. Carefully transfer the whole thing to the oven and bake about 60 minutes, until the centre is set (it will still jiggle a little bit, but not much).

Remove the springform pan from the water bath and place onto a wire rack to cool to room temperature, about 2 hours. Transfer to fridge until ready to serve (up to 48 hours in advance).

Combine sugar and water in a 10" frying pan over medium heat. Whisk just until sugar dissolves, then stop. Gently tilt and swirl the pan occasionally until the mixture bubbles down to a syrup and turns amber in colour, about 10 minutes. If you're nervous, reduce the heat to low so you have more control - it'll just take a few minutes longer.

Remove pan from heat and whisk in the butter and the cinnamon. Be extremely careful, as the caramel may sputter. Quickly add the apples and stir to coat in caramel. Return the pan to medium heat. The caramel may seize up a bit, but not to worry - keep stirring and it will melt back down. Cook, stirring often until the apples are tender, about 7 minutes. Stir in the vanilla. Use a spatula to scrape apples into to a shallow pan or bowl to cool then refrigerate until ready to serve.