Preheat the oven to 325°F (163°C) and grease a 9-inch springform pan.
In a mixing bowl, combine graham cracker crumbs, melted butter, and brown sugar. Press the mixture firmly into the bottom of the pan.
Bake the crust for 10 minutes, then remove from the oven and let cool.
In a large mixing bowl, beat the cream cheese, granulated sugar, and brown sugar until smooth.
Add the eggs one at a time, mixing well after each addition.
Stir in the vanilla extract.
Melt the butterscotch chips with heavy cream in the microwave in 30-second intervals, stirring until smooth.
Mix the melted butterscotch into the cheesecake batter until fully incorporated.
Pour the batter over the cooled crust and smooth the top.
Bake for 50-55 minutes, or until the center is set but slightly jiggly.
Turn off the oven and let the cheesecake cool inside with the door slightly open for 30 minutes.
Refrigerate for at least 4 hours before serving.
Top with butterscotch sauce and whipped cream before serving.