In a heavy saucepan, stir together the milk and 1/4 cup of sugar. Bring to a boil over medium heat.
In a medium bowl, whisk together the egg yolks and egg. Stir together the remaining sugar and cornstarch; then stir them into the egg until smooth. When the milk comes to a boil, drizzle it into the bowl in a thin stream while mixing so that you do not cook the eggs. Return the mixture to the saucepan, and slowly bring to a boil, stirring constantly so the eggs don' t curdle or scorch on the bottom.
When the mixture comes to a boil and thickens, remove from the heat. Stir in the butter and vanilla, mixing until the butter is completely blended in. Pour into a heat-proof container and place a piece of plastic wrap directly on the surface to prevent a skin from forming. Refrigerate until chilled before using.