Preheat the oven to 350 degrees. Spray a 13- by 9-inch baking pan with cooking spray (or line with parchment paper) and set aside.
Press the cookie dough into an even layer in the bottom of the pan and bake for 22 to 28 minutes, until the edges are set and the top is golden. Place on a wire rack and cool completely before proceeding.
Place the butter in a medium saucepan and melt over medium heat. Stir in the sugar and evaporated milk, then bring to a simmer. Simmer 4 to 5 minutes, stirring constantly, then remove from the heat.
Stir in the marshmallow creme, peanut butter, and vanilla and stir until completely combined. Stir in the chopped peanuts and spread over the cooled cookie layer. Refrigerate until set, about 1 hour.
Combine the caramel and heavy cream in a small saucepan and stir over low heat until caramels are melted and mixture is smooth. The caramels will look like they don’t want to melt at first; just keep stirring and they’ll get there.
Spread over the nougat layer and refrigerate until set, about 30 minutes.
Place the chocolate chips, butterscotch chips, and peanut butter in a microwave-safe bowl and microwave, stirring often, until chips are melted and mixture is smooth. Pour over the caramel layer and refrigerate for at least 1 hour (overnight is better). Use a very sharp knife to slice into bars. Serve.