In a small saucepan, whisk together the eggs and egg yolks. Then whisk in the lemon juice, lemon zest, sugar, and cornstarch.
Place the saucepan on the stove and turn the heat to medium low. You will need to whisk the mixture constantly as it heats. Keep whisking and cooking the mixture until it thickens to the point that it will coat the back of a spoon. If you have an instant read thermometer, you want it to reach 170 °F (77 °C). (It may take up to 10 minutes, and remember that it will continue to thicken when it is chilled.) You must whisk it constantly, even while checking the temperature.
Once the curd has thickened, remove the pan from the heat. Stir in the butter until it is incorporated, then stir in the vanilla.
If the lemon curd is not completely smooth, you will want to strain it through a fine mesh sieve.
Allow the curd to cool for about 15 minutes. Then place a piece of plastic wrap directly on the surface of the curd (so it doesn’t develop a film) and place this into the fridge. It should chill for at least 3 hours.