Line a 9x13-inch pan with parchment or lightly grease for easy removal.
Stir cookie crumbs, melted butter, and a pinch of salt until the mixture looks like wet sand.
Press crumbs firmly into the pan to form an even crust. Chill 10 minutes.
Beat cream cheese until smooth. Mix in peanut butter, powdered sugar, and vanilla until fluffy.
Fold in about half the whipped topping. Spread this layer over the crust. Chill 10 minutes.
Whisk pudding mix with cold milk for 2 minutes. Let stand 3 minutes to thicken.
Spread pudding over the peanut butter layer. Top with remaining whipped topping.
Scatter chopped peanut butter cups over the top and drizzle with chocolate syrup.
Cover and refrigerate at least 4 hours, or until set. Slice and serve chilled.