Whisk together first 6 ingredients in a heavy 3-quart saucepan until smooth. Bring mixture to a boil over medium heat, whisking constantly; boil 1 minute or until thickened. Remove from heat; whisk in butter and vanilla extract. Place a sheet of wax paper directly on surface of mixture to prevent a film from forming, and chill 4 hours.
Note: To chill filling quickly, pour filling into a bowl. Place bowl in a larger bowl filled with ice. Whisk constantly until cool (about 15 minutes).