Preheat the oven to 140℃ (285℉). Line a baking sheet with parchment paper.
Take 1 apple and, starting from the bottom, slice it thinly through the core - use a mandoline if you have one to get thin, even slices or use a very sharp knife. Place the apple slices on the baking tray, making sure not to overlap them.Bake for 45 to 55 minutes, turning them over once, or until they're dry to touch and beginning to curl up (thicker slices will take longer to crisp, so keep an eye on them to make sure they do not brown too much).Transfer the apple crisps to a wire rack to cool completely.
Increase the oven temperature to 180℃ (350℉). Spray a 20 x 20-cm (8 x 8-inch) with baking spray and line the bottom with parchment paper.
To make the cake, peel, core, and roughly chop the 2 apples and place them into a small sauce, along with the water. Cook over a low heat for 8 to 10 minutes, or until the apples have softened. Remove from the heat and mash them lightly with a fork to make applesauce (it's fine to have a few chunkier pieces). Set aside.
Using a stand mixer, whisk together the eggs and the sugar for 2 to 3 minutes, or until the eggs are pal and thick. With the mixer still running, slowly pour in the oil and continue to beat for another minute. Stir in the applesauce, vanilla, flour, baking powder, baking soda, and cinnamon. Pour the batter into the prepared pan and bake for 35 to 40 minutes, or until the cake is well browned and springy to the touch.Remove from the oven and allow to cool completely in the pan.
To make the sage caramel, add the cream and sage leaves to a small saucepan. Bring to a simmer, and then remove from the heat, cover and let it steep and cool for 20 minutes. Once cool, discard the sage leaves.
In a separate saucepan, heat the granulated sugar over a medium heat until it dissolves and turns a light amber colour (swirl the pan every now and again to help the sugar caramelise evenly). Once it reaches a golden amber colour, slowly pour in the cream (be careful, as the caramel will bubble up rapidly). Whisk constantly and let the caramel simmer for 30 seconds before removing it from the heat and stirring in the salt. Pour it into a bowl to cool.
To make the frosting, add the butter and powdered sugar to the bowl of an electric mixer, and beat until the mixture is pale and creamy. Add the cream cheese and beat for 1 minute, or until smooth. Beat in 60g (3 tablespoons) of the sage caramel and set aside until you are ready to decorate.
When the cake is completely cool, remove it from the pan and pace it on a cake stand or serving plate. Spoon on the frosting, spreading it evenly and leaving about a 1 cm border around the edges. Drizzle on the remaining sage caramel and then place the apple crisps, sage leaves, and walnuts on top.
