In a medium bowl, whisk together egg and egg yolks.
Sift in corn starch and sugar.
Mix well.
In a 2 quart saucepan over medium low heat, heat coconut milk until it just starts to bubble around the edge.
Remove from heat.
Whisk into egg mixture in small amounts.
Return entire mixture to saucepan.
Heat, stirring constantly, until mixture is thick and coats a spoon, about 12-15 minutes.
Remove from heat.
Whisk in butter and vanilla.
Continue whisking until completely smooth.
Spoon into desired serving glasses. Set aside or refrigerate.