Start by preheating your oven to 325°F. Mix graham cracker crumbs, brown sugar, and melted butter until combined. Press the mixture evenly into the bottom and slightly up the sides of a springform pan, then bake for 8–10 minutes and let cool.
Lower the oven temperature to 300°F. Beat cream cheese, sugar, and flour until smooth. Add vanilla, sour cream, and blend until creamy. Warm heavy cream and butterscotch chips together and stir into the mixture, then fold in eggs gently.
Wrap the springform pan in foil and place it in a larger pan with hot water halfway up the sides. Bake until the center is just set, about 60–70 minutes. Let cool slightly, then refrigerate for at least 4 hours or overnight.
Melt butterscotch chips with heavy cream in short microwave bursts, stirring until silky smooth. Pour over the chilled cheesecake, spreading evenly, and let it set in the fridge for 30 minutes before serving.