Preheat your oven to 350°F (175°C). In a bowl, mix together graham cracker crumbs, melted butter, and brown sugar until combined. Press this mixture firmly into the bottom of a 9-inch springform pan to create an even crust.

Bake for about 10 minutes, then remove from oven and allow it to cool.

In a large mixing bowl, beat the softened cream cheese until smooth. Gradually add the brown sugar and continue mixing until well incorporated.

Add the sour cream, eggs one at a time, and vanilla extract, mixing until smooth. Gently fold in the butterscotch chips.

Pour the cheesecake filling over the cooled crust in the springform pan. Smooth the top with a spatula.

Bake in the preheated oven for 55-60 minutes. The cheesecake should be slightly jiggly in the center. Turn off the oven and let it cool inside for an hour, then refrigerate for at least 4 hours or overnight.

In a saucepan, melt the butter over medium heat. Stir in the brown sugar and a pinch of salt, cooking until well combined.

Slowly pour in the heavy cream, continually stirring until smooth. Remove from heat and stir in the vanilla extract.

Carefully remove the cheesecake from the springform pan. Slice and drizzle with the warm butterscotch sauce before serving.