Place cornstarch in a medium-sized bowl. Add ½ cup of the milk (measure #1) and whisk until cornstarch is dissolved.
Add the egg and egg yolks to the cornstarch/milk mixture. Whisk lightly until combined.
Combine remaining milk (measure #2) and granulated sugar in a medium-sized saucepan. Heat over medium heat until the mixture reaches a low boil. Remove from heat.
Slowly pour ½ cup of the hot mixture into the egg mixture; whisking constantly.
Return the remaining milk/sugar mixture to a simmer over medium-low heat. Slowly pour the egg mixture into the saucepan, whisking constantly.
Continue to whisk vigorously until the mixture is quite thick (3 - 5 minutes). The continuous whisking is important in this step. The eggs will curdle if not whisked properly - which results in a lumpy, eggy pastry cream.
Remove from heat. Add the butter and vanilla. Whisk until all the butter is melted.
Pour into a heatproof bowl. Place plastic wrap directly over top of pastry cream to prevent a skin from forming.
Notes
Keep pastry cream refrigerated until ready to use.