Preheat oven to 325°F (160°C). Grease a 9-inch springform pan.
Make the crust: In a bowl, mix graham cracker crumbs and brown sugar. Add melted butter and stir until combined. Press the mixture into the bottom of the springform pan and bake for 10 minutes. Let it cool.
Prepare the filling: In a large bowl, beat softened cream cheese and sugar until smooth. Add eggs, one at a time, beating well after each addition. Mix in vanilla extract, butterscotch sauce, and heavy cream until the mixture is creamy and well-blended.
Bake the cheesecake: Pour the cheesecake batter over the cooled crust. Bake for 55-60 minutes, or until the center is set. Turn off the oven and let the cheesecake cool inside with the door slightly open for about 1 hour. Once cooled, refrigerate for at least 4 hours or overnight.
Make the Butterbeer topping: Whip heavy cream and powdered sugar until soft peaks form. Gently fold in the butterscotch sauce and vanilla extract. Spread the topping over the chilled cheesecake and sprinkle with gold sprinkles if desired.
Serve: Slice and enjoy your Hogwarts Butterbeer Cheesecake, transporting yourself to the magical halls of Hogwarts!
