Preheat oven to 350 degrees F. Line a 9x13-inch baking pan with parchment paper; set aside.
Make the Base: In a large bowl, whisk together the melted butter, sugar and eggs. Use a large wooden spoon to stir in the graham cracker crumbs, coconut and cocoa powder until completely combined. Transfer to prepared baking pan and press evenly into pan. (The mixture will be a little sticky, so you may need to wet your fingers a bit and then press it in.) Bake for 12 to 15 minutes, or until firm and no longer shiny. Transfer to a cooling rack and allow to cool completely before preparing the filling.
Make the Filling: Microwave the peanut butter and butter in a large bowl until completely melted and smooth. Whisk in the powdered sugar 1 cup at a time, alternating with the milk in two additions, whisking until smooth. Spread evenly over the base and refrigerate until firm, about 1 hour.
Make the Topping: Using a double boiler (or a microwave on 50% power), melt the chocolate and butter. Spread over the filling and allow to set at room temperature (or refrigerate to speed up the process) before cutting into bars and serving. Leftovers should be stored in an airtight container at room temperature or in the refrigerator.