Blend avocado and melted butter together in a blender until completely smooth; pour into a saucepan and place over low heat.
Stir cocoa powder, melted chocolate chips, Irish cream liqueur, and vanilla extract into the avocado mixture until smooth. Add 3 cups confectioners' sugar in small amounts, stirring each addition completely into the avocado mixture before introducing the next; cook and stir until thick and smooth, 5 to 10 minutes.
Grease a baking dish. Pour the fudge batter into the baking dish and smooth with a spatula into an even layer. Sprinkle chopped walnuts atop the fudge and dust with 1 tablespoon confectioners' sugar.
Refrigerate fudge until firmly set, at least 1 hour.