Preheat the oven to 350°F (175°C) and lightly coat a 9x13-inch baking dish with cooking spray.

In a saucepan over low heat, gently melt the butterscotch chips together with the butter, stirring often to prevent scorching, for approximately 5 minutes. Remove from the heat and blend in the graham cracker crumbs until thoroughly combined. Reserve 2/3 cup of this mixture and press the remainder firmly into the base of the prepared baking dish to create an even crust.

In a mixing bowl, beat the softened cream cheese with an electric mixer until it becomes light and airy. Add the sweetened condensed milk, the egg, and vanilla extract; continue mixing until smooth and homogeneous.

Evenly pour the cream cheese mixture over the prepared crust, then scatter the reserved graham cracker-butterscotch blend across the top as a crumbly topping.

Bake in the preheated oven for 25 to 30 minutes, or until a knife inserted into the center emerges clean. Allow to cool before slicing into bars.