Beat eggs in the bowl of an electric mixer fitted with the whisk attachment until frothy, 1-2 minutes.
In a small saucepan, heat sugar and water to 244℉/118℃.
With the mixer running, stream sugar syrup into eggs.
Continue beating until cool, 3-4 minutes.
While mixture is beating, melt chocolate.
When mixture has cooled, beat in chocolate and vanilla.
Add butter in small amounts while continuing to beat.
Beat until completely smooth.
Spoon into a pre-baked 9 inch pie shell and spread evenly.