Preheat the oven to 350 degrees F.
Place the graham crackers, 1/2 cup of the walnuts and brown sugar in a food processor and process until finely ground. With the motor running, add the butter through the feed tube and process until the mixture just comes together. Spray the bottom and side of the pan with cooking spray. Pat the mixture evenly into the bottom of a 9-inch springform pan, place on a baking sheet and bake in the oven until lightly golden brown and just set, about 8 minutes. Remove to a baking rack and let cool completely.
Combine 1/4 cup of the sugar and the orange zest in a food processor and process until combined.
Place the cream cheese in the bowl of a stand fixer fitted with the paddle attachment and beat until light and fluffy, 3 to 4 minutes. Add the orange sugar, remaining granulated sugar, and light muscovado sugar and beat again until the sugar is incorporated and the mixture is light and fluffy. Add the eggs, 1 at a time and mix until just incorporated, scraping the sides and bottom of the bowl. Add the vanilla seeds and vanilla extract and beat until combined. Add the salt and heavy cream and mix until just combined.
Scrape the mixture into the prepared pan. Set the cheesecake pan on a large piece of heavy duty aluminum foil and fold up the sides around it. Place the cake pan in a large roasting pan. Pour hot tap water into the roasting pan until the water is about halfway up the sides of the cheesecake pan; the foil will keep the water from seeping into the cheesecake. Bake until the sides of the cake are slightly puffed and set and the center still jiggles, about 55 minutes.
Turn the heat off and prop the door open with a wooden spoon and allow the cake to cook in the water bath for 1 hour. Remove the cake to a baking rack and allow to cool to room temperature for 2 hours. Cover the cake and refrigerate for at least 4 hours and up to 24 hours until chilled through.
Top with the warm apple topping, drizzle liberally with the caramel sauce and sprinkle with the remaining toasted walnuts. Serve additional sauce on the side.
Bring apple juice, sugar and vanilla bean to a boil in a large saute pan over high heat and cook until slightly thickened and reduced to 1/2 cup. Stir in the butter until melted. Add the apples and cook, stirring occasionally, until lightly caramelized and soft. Add the apple brandy and cook until reduced by 1/2. Transfer the apples to a plate and let cool slightly.
Place sugar and water in a medium saucepan and bring to a boil over high heat (do not stir), swirling the pot occasionally to even out the color, until amber in color, 10 to 12 minutes.
While the caramel is cooking. Place the heavy cream in a small pan and bring to a simmer over medium heat. Remove from heat and keep warm.
When the caramel has reached the desired color, slowly whisk in the heavy cream and salt and whisk until smooth. Remove from the heat and stir in the apple brandy and vanilla extract. Keep warm.