In a medium saucepan, heat the butter and lemon juice over medium heat until the butter melts and the mixture is hot, about 130°F on a thermometer.

Meanwhile, in a medium bowl, whisk the eggs, egg yolks, and sugar together to blend them, then whisk in the dissolved cornstarch. Whisking constantly, slowly pour the hot butter and lemon juice into the yolk mixture. Return the mixture to the saucepan and cook over medium heat, stirring constantly with a large spoon, just until it comes to a boil and thickens; it will take about 6 minutes. When thickened, the sauce will leave a path on the back of the spoon if you draw your finger across it and look clear rather than cloudy. Immediately remove from the heat, strain into a small bowl, and stir in the lemon zest. Press plastic wrap directly onto the surface of the sauce, use a toothpick to poke a few holes in the plastic wrap to let steam escape, and refrigerate until cold. The sauce will thicken further as it chills.

The sauce can be refrigerated for up to 3 days. Or, spoon the cold sauce into a plastic freezer container, leaving at least an inch of space in the top of the container, press plastic wrap onto the surface, seal tightly, and freeze for up to 3 months.