Line an 8 by 8-inch baking pan or casserole with aluminum foil, with long flaps hanging over each edge.
For the cookie: Put the butter in a heatproof medium bowl. Bring a saucepan filled with an inch or so of water to a very slow simmer over medium-low heat. Set the bowl over, but not touching, the water. Once the butter is melted, add the sugar and cocoa, and stir to combine. Add the egg and cook, stirring constantly with a whisk, until warm to the touch and slightly thickened (it should be about the consistency of hot fudge), about 6 minutes. Remove from the heat and stir in graham crumbs, coconut and nuts. Press the dough firmly into the prepared pan. (Save the pan of water for melting the chocolate.)
For the filling: Beat the butter, peanut butter and confectioners' sugar together in a medium bowl with an electric mixer until light. Spread over the cookie and freeze while you prepare the chocolate glaze.
For the glaze: Put the chocolate and butter in a medium heatproof bowl, and set over the barely simmering water. Stir occasionally until melted and smooth. Remove from the heat and let cool slightly. (Alternatively, put the chocolate and butter in a medium microwave-safe bowl. Melt at 50 percent power in the microwave until soft, about 1 minute. Stir, and continue to heat until completely melted, about 1 minute more.). When cool but still runny, pour the chocolate layer over the chilled peanut butter layer and carefully smooth out with an offset spatula. Freeze 30 minutes.
To serve, remove from the freezer and let sit at room temperature for 5 minutes. Pull out of the pan using the foil flaps and transfer to a cutting board. Cut into 1-inch squares with a sharp knife. Serve cool or at room temperature.
Finished bars can be wrapped in the pan in plastic wrap, then aluminum foil and frozen for up to 1 month.
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