Combine butter, cocoa, and sugar in a saucepan.

Cook over low heat until blended, stirring constantly.

Add vanilla extract and beaten egg.

Continue cooking for 5 minutes, stirring continuously.

Stir in graham cracker crumbs and nuts until well combined.

Press the mixture into a buttered 9-inch pan.

Allow the first layer to cool completely.

For the second layer, cream together butter and milk.

Add instant vanilla pudding and mix well.

Gradually add powdered sugar and beat until smooth and creamy.

Spread the second layer evenly over the cooled first layer.

Let the second layer set.

For the third layer, melt chocolate chips and butter in a double boiler or microwave.

Stir until smooth and completely melted.

Spread the melted chocolate mixture evenly over the second layer.

Score the top layer into squares while the chocolate is still soft.

Refrigerate the cookies until firm before serving.