In a medium bowl, combine graham cracker crumbs, melted butter, and sugar, mixing until evenly blended. Press this mixture firmly into the bottom of a greased 9 x 13 inch pan, ensuring it's compact and even across the surface.

In a separate bowl, beat together softened cream cheese, creamy peanut butter, and powdered sugar until the mixture is smooth and creamy. Gradually fold in the heavy whipping cream, creating a light and airy texture.

Spoon the peanut butter mixture over the crust using a wet spatula to evenly spread and level it out.

In a large bowl, whisk together the instant vanilla pudding mix and instant chocolate pudding mix with milk until the mixture thickens, about 2-3 minutes. Carefully pour this thick pudding over the creamy peanut butter layer.

Gently spread the thawed Cool Whip over the pudding layer using a spatula. Sprinkle chopped peanut butter cups on top.

Cover the dessert with plastic wrap and refrigerate for at least 2-4 hours, or until the layers are set and chilled.