In a mixing bowl, combine the chocolate wafer crumbs, sugar, and melted butter. Mix until the crumbs are well-coated and the mixture resembles wet sand. Press the mixture firmly into the bottom of your pie dish or individual cups to form an even layer. Place the crust in the refrigerator to set while you prepare the filling.
Using a double boiler or microwave, melt the semisweet chocolate chips until smooth. If using a microwave, heat in 30-second intervals, stirring in between to prevent burning. Once melted, let it cool slightly while you prepare the rest of the filling.
In a separate bowl, whisk together the egg yolks until they are pale and slightly thickened. This will help create a creamy texture in your filling.
Gradually add the melted chocolate to the egg yolks, whisking continuously to prevent the eggs from cooking. In another bowl, whip the heavy cream until it forms soft peaks, then fold in the vanilla extract. Gently fold the whipped cream into the chocolate mixture until combined.
Pour the chocolate filling into the prepared crust, smoothing the top with a spatula. Cover with plastic wrap and refrigerate for at least 4 hours, or until set. This step is crucial for achieving that perfect velvety texture.
In a mixing bowl, beat the softened butter until creamy. Gradually add the confectioners' sugar and cocoa powder, mixing until smooth. Add milk, one tablespoon at a time, until you reach your desired consistency for spreading or piping.
Once the filling is set, spread the cocoa buttercream over the top of the dessert. You can also pipe it on for a prettier presentation. Optionally, garnish with chocolate shavings or fresh berries for an extra touch. Slice, serve, and watch as your guests savor every bite of this Chocolate Velvet Dessert!