1. Prepare the Graham Cracker Crust

1. Preheat Oven: Preheat your oven to 325°F (163°C). Lightly grease a 9-inch springform pan and line the bottom with parchment paper for easy removal.
2. Make the Crust Mixture: In a mixing bowl, combine graham cracker crumbs, melted butter, and sugar. Stir until the mixture resembles wet sand.
3. Press into Pan: Press the mixture firmly into the bottom of the prepared springform pan, creating an even layer. Use the back of a spoon or the bottom of a glass to pack it tightly.
4. Bake and Cool: Bake the crust for 10 minutes. Remove from the oven and set aside to cool while you prepare the filling.

2. Prepare the Butterscotch Cheesecake Filling

1. Melt the Butterscotch Chips: Place the butterscotch chips in a microwave-safe bowl. Heat in 20-second intervals, stirring after each interval, until the chips are melted and smooth. Let cool slightly.
2. Beat the Cream Cheese: In a large mixing bowl, beat the softened cream cheese with a hand or stand mixer on medium speed until smooth and creamy, about 2 minutes.
3. Add Sugars: Add the granulated sugar and brown sugar to the cream cheese, and beat until well combined and fluffy.
4. Incorporate the Butterscotch: Slowly add the melted butterscotch chips to the mixture, beating on low speed until fully incorporated.
5. Add Eggs and Vanilla: Add the eggs, one at a time, mixing on low speed after each addition. Then mix in the vanilla extract.
6. Add Heavy Cream: Pour in the heavy cream and mix just until combined. Do not overmix to avoid incorporating too much air.

3. Assemble and Bake the Cheesecake

1. Pour Filling Over Crust: Pour the cheesecake batter over the cooled crust, spreading it evenly.
2. Water Bath (Optional): For a crack-free cheesecake, place the springform pan in a larger roasting pan. Fill the roasting pan with hot water until it reaches halfway up the sides of the springform pan.
3. Bake: Bake the cheesecake at 325°F (163°C) for 55-65 minutes, or until the edges are set and the center is slightly jiggly.
4. Cool Gradually: Turn off the oven and crack the door open slightly. Let the cheesecake cool in the oven for 1 hour to prevent cracking.

4. Chill the Cheesecake

1. Refrigerate: Once the cheesecake has cooled to room temperature, cover it with plastic wrap or foil and refrigerate for at least 6 hours or overnight for the best flavor and texture.

5. Prepare the Butterscotch Sauce

1. Melt Chips and Cream: Combine the butterscotch chips and heavy cream in a microwave-safe bowl. Heat in 20-second intervals, stirring after each interval, until smooth and creamy.
2. Cool Slightly: Let the sauce cool to room temperature before drizzling over the cheesecake.

6. Decorate and Serve

1. Drizzle and Add Toppings: Before serving, drizzle the cheesecake with the butterscotch sauce and sprinkle with your choice of toppings, such as crushed toffee bits or chopped nuts.
2. Slice and Enjoy: Use a sharp knife dipped in hot water (and wiped clean) for clean slices. Serve chilled.