In small bowl, cream together butter and sugar until light and fluffy. Add melted chocolate and vanilla. Beat until smooth. Add 1 egg and beat 5 minutes. Add remaining egg and beat 5 more minutes. Pour mixture into crust (crust must be cool) and chill until set, about 3 hours. Spread with whipped cream if desired.
Note: I wouldn't attempt this without a good stand mixer. The "silk" in the name refers to the texture, provided the filling is beaten until the sugar is *completely* dissolved. It takes a long time to cream the butter and sugar properly, and 5 minutes after each egg is a minimum.
We use a straight-sided 9 " cake pan and usually make at least 1-1/2 recipes of filling. In doing this the mixer is running almost continually for 30-40 minutes. I'm not sure it's possible to overbeat it, but I know that if it's not beaten long enough, it's grainy.
For the crust, proceed as for a graham cracker crust, but use Nabisco chocolate wafers (don t remember the name); they re thin and crisp.