Preheat oven to 350°F (175°C).

Grease a 13 x 9 inch cake pan.

Line the pan with parchment paper, leaving an inch extending over the long edges.

In a large bowl, whisk together eggs, 1 cup melted butter, cocoa, and sugar.

Stir in graham cracker crumbs, shredded coconut, and finely chopped walnuts.

Press the mixture evenly into the prepared pan.

Bake for 10 minutes.

Cool completely in the pan on a wire rack.

In a medium bowl, stir together the remaining 1/3 cup melted butter, milk, and vanilla.

Beat in confectioners' sugar until smooth.

Spread the mixture evenly over the cooled base.

Refrigerate until firm, about 45 minutes.

Place chopped chocolate and the remaining 2 tablespoons of butter in a microwave-safe bowl.

Heat for 1 minute, then stir.

Heat in 30-second intervals, stirring until melted and smooth.

Spread the melted chocolate evenly over the filling.

Score the surface into serving-size pieces.

Refrigerate until set, about 1 hour.

Use the parchment paper to lift the bars from the pan and peel off the paper.

Cut into individual bars.