Preheat oven to 350°F (175°C). Line a 9×9-inch baking pan with aluminum foil for easier cleanup and spray with cooking spray; set aside.
In a medium saucepan, add the butterscotch chips and butter. Heat over medium to medium-low heat, whisking nearly the entire time for at least 5 minutes until the chips melt and the mixture becomes smooth and emulsified.
Add the graham cracker crumbs to the melted butterscotch mixture and stir to combine. Remove 1 heaping cup of the butterscotch crumb mixture and set aside in a small bowl.
Transfer the remaining butterscotch crumbs to the prepared pan and evenly hard-pack them to form a smooth crust; set aside.
In the bowl of a stand mixer or a large mixing bowl using a handheld electric mixer, add the cream cheese and beat on high power until smooth and fluffy, about 2 to 3 minutes. Stop to scrape down the sides of the bowl.
Add the egg, sweetened condensed milk, vanilla, and salt, and beat to incorporate. Note: It’s normal to see a few small blobs of cream cheese floating and seeming difficult to break down and incorporate into the mixture. Keep beating for another minute or two and they will diminish.
Evenly pour the mixture over the crust.
Evenly sprinkle the reserved butterscotch mixture over the top and bake for about 32 to 35 minutes, or until the top is set. It will still be a little jiggly but springy to the touch. Start checking at 25 to 30 minutes because all ovens vary; conversely, if it takes longer for yours to bake and set up, don’t fret.
Allow the bars to cool in the pan for about 1 hour at room temp before covering and refrigerating until well chilled before serving.