Prepare an ice bath; set aside. In a medium bowl, combine egg yolks, egg, and 2 tablespoons sugar. Add cornstarch and flour; whisk until smooth and pale yellow. Set aside.
In a medium saucepan, combine milk and remaining 3/4 cup sugar. Stir over medium-high heat until milk begins to steam. Whisking constantly, add half the hot milk to the egg-yolk mixture. Stir until smooth; add combined mixture back to remaining hot milk in the pan. Bring mixture to a boil, whisking rapidly to prevent scorching. Remove from heat, and stir in butter and vanilla. Strain through a fine sieve into a medium bowl.
Place over ice bath and let stand, stirring frequently, until cool. Remove from ice bath, and press a piece of plastic wrap directly onto surface until ready to use. If not using immediately, refrigerate in an airtight container for up to 3 days.