Make the crust

1. Heat the oven to 325°F (163°C). Line the base of a 9-inch (23 cm) springform pan with parchment and grease the sides.
2. Stir the graham crumbs, brown sugar, and melted butter until the mixture resembles wet sand. Press it firmly into the bottom and a little way up the sides of the pan.
3. Bake the crust 8–10 minutes, then remove and let cool. Wrap the outside of the pan in aluminum foil so the water bath won’t seep in; set the prepared pan aside.

Prepare the filling

1. Lower the oven temperature to 300°F (148°C).
2. In a large bowl, beat the room-temperature cream cheese with the brown sugar and flour on low speed just until smooth. Scrape down the bowl so everything mixes evenly. (Mixing slowly helps keep air out and reduces cracking.)
3. Add the vanilla and sour cream and blend on low until incorporated. Set the bowl aside.
4. In a microwave-safe bowl, combine the heavy cream and 1 cup butterscotch chips. Heat in 15–30 second bursts, stirring between each, until the chips have melted and the mixture is silky. Let it cool slightly.
5. Pour the melted butterscotch mixture into the cream cheese in two pours, mixing gently after each addition.
6. Sprinkle in the dry butterscotch pudding mix and blend until evenly distributed.
7. Add the eggs one at a time, mixing briefly after each and scraping the sides of the bowl.

Bake with a water bath

1. Pour the filling into the chilled crust. Place the springform pan inside a larger roasting pan. Carefully pour warm water into the outer pan until it reaches about halfway up the side of the springform (do not let water top the foil).
2. Bake 1 hour 30 minutes to 1 hour 35 minutes, until the perimeter looks set and the middle still has a slight jiggle.
3. Turn the oven off and leave the cheesecake inside, door closed, for 30 minutes. Then crack the oven door and let it sit another 10 minutes. This slow cooldown helps prevent cracks.
4. Remove the cheesecake to a rack and let it reach room temperature. Chill in the refrigerator until firm — at least 5–6 hours, preferably overnight.

Finish and serve

1. When the cake is cold, release it from the springform and transfer to a serving plate.
2. For the ganache: place 1 cup butterscotch chips in a heatproof bowl. Warm 4 1/2 tablespoons heavy cream until it begins to steam (just shy of boiling) and pour it over the chips. Let sit 2–3 minutes, then whisk until glossy and smooth.
3. Let the ganache cool 4–6 minutes until slightly thickened but still pourable, then spread over the cheesecake. Scatter extra butterscotch chips on top if desired. Refrigerate until ready to slice.