Combine eggs, yolks, and 1/2 cup sugar in bowl of electric mixer fitted with whisk attachment. Beat on medium-high speed until mixture is pale yellow and thick, 2 to 3 minutes. Turn off machine. Sift in cornstarch; beat on medium low speed until combined.
Meanwhile, bring milk and remaining 1/4 cup sugar to a boil in a medium saucepan. Whisking constantly, slowly pour half of milk mixture into egg mixture; continue to whisk until smooth. Pour mixture back into saucepan; set over medium heat.
Whisk over medium heat another 2 to 3 minutes, until mixture reaches the consistency of matonnaise. Transfer to a large bowl. Add butter, 1 tablespoon at a time, stirring until melted after each addition. Set over an ice bath until chilled. Stir in vanilla. Cover with plastic wrap and let chill overnight or at least 2 hours before using.