Combine water, sugar and cream of tartar in a thick saucepan and mix well. Clip candy thermometer. Cook over medium high heat until syrup reaches 250 degrees °F.
Start beating the egg yolks when temperature of the sugar mixture reached 220 degrees.
Beat egg yolks until thick and lemon-colored.
When syrup temperature reaches 250 degrees, remove from fire and add syrup in thin streams to the egg yolks, while beating at high speed. Chill.
In another bowl, cream butter until light and fluffy.
Gradually add the chilled egg yolk mixture to the butter while beating at medium speed. Wait for the butter to absorb the yolk mixture before adding the next spoonful or so.
Add vanilla. Refrigerate until ready to use.