Combine the graham cracker crumbs, melted butter, and granulated sugar in a bowl until the mixture resembles wet sand. Press the mixture firmly into a lightly greased 9x13-inch baking dish and chill for 10 to 15 minutes.

Beat the softened cream cheese and creamy peanut butter together until smooth. Gradually add the powdered sugar and vanilla extract, then fold in the thawed whipped topping. Spread the peanut butter mousse evenly over the chilled crust.

Place the semi-sweet chocolate chips in a heatproof bowl. Heat the heavy cream until steaming, pour it over the chocolate chips, and let it sit for 2 to 3 minutes. Whisk until smooth and glossy. Let the ganache cool for 10 to 15 minutes.

Pour the slightly thickened ganache over the peanut butter mousse layer and spread evenly to cover the surface.

Cover the dish and refrigerate for at least 4 hours, preferably overnight, until the layers are fully set. Before serving, garnish with chopped peanuts, halved chocolate-peanut butter candies, and chocolate shavings.

Slice the dessert with a sharp knife and serve chilled directly from the refrigerator.