Have eggs ready in a bowl, and set aside where it will be within reach.

Using a whisk, combine milk, sugar and cornstarch in a medium saucepan over medium heat on stovetop. Allow milk to scald (heat to the point when tiny bubbles form around edges of pan). Whisk occasionally to prevent cornstarch from clumping on bottom edges of pan.

Remove milk mixture from heat, preferably to a burner that's turned off.

Mix about 2 tablespoons of scalded milk mixture into eggs using whisk, then introduce eggs into milk mixture in a slow stream, whisking milk mixture constantly.

Immediately return pan to heat and whisk gently until custard thickens, another two or three minutes. Do not allow to boil. (If you find that you have egg white strands in custard, feel free to pass it through a fine-mesh sieve into a different bowl now.)

Remove pan from heat and stir in vanilla.