Preheat an oven to 350 degrees F (175 degrees C). Mix the chocolate cookies with the butter and cinnamon in a bowl. Press mixture firmly into the bottom of a 9-inch springform pan.
Bake in the preheated oven until the crust hardens, about 8 minutes. Set aside to cool.
Beat together the cream cheese, confectioners' sugar, and vanilla extract. Stir in the peanut butter until well blended, then fold in 3 cups whipped topping until the mixture is light and fluffy. Transfer the mixture onto the cooled cookie crust, spreading evenly on top.
Place the remaining 3/4 cup whipped topping into a pastry bag with a tip. Pipe the topping on the pie decoratively. Drizzle the chocolate and caramel syrups on top, and sprinkle with chopped peanut butter cups.
