Prepare an 8x8 inch baking pan by lining it with parchment paper. Leave a slight overhang on the edges to make removing the bars easier later.

In a heatproof bowl set over a pot of simmering water, melt 1/2 cup of butter, granulated sugar, and cocoa powder. Whisk in the lightly beaten egg and stir continuously until the mixture thickens slightly, about 2 to 3 minutes.

Remove the bowl from the heat and stir in the graham cracker crumbs and shredded coconut until well combined. Press the warm mixture firmly and evenly into the bottom of the prepared pan, then chill in the refrigerator for 20 minutes.

In a medium mixing bowl, use an electric mixer to beat the softened butter and creamy peanut butter until completely smooth. Add the heavy cream and powdered sugar, beating until the filling is light, fluffy, and spreadable.

Spread the peanut butter filling evenly over the chilled bottom layer using a rubber spatula. Return the pan to the refrigerator to chill for another 20 minutes until the center feels firm to the touch.

Place the chopped semi-sweet chocolate and 2 tablespoons of butter into a microwave-safe bowl. Microwave in 30-second increments, stirring well after each interval until the chocolate is completely melted, smooth, and glossy.

Pour the melted chocolate over the chilled peanut butter layer, spreading it quickly into a smooth, even layer. Chill in the refrigerator for at least 1 hour before lifting the block out by the parchment paper, slicing into neat squares, and serving cold!