In a medium saucepan, whisk together eggs, sugar, lemon juice, and lemon zest.

Cook over medium-low heat, whisking constantly, until the mixture thickens enough to coat the back of a spoon, about 8-10 minutes.

Remove from heat and whisk in butter one piece at a time until smooth.

Strain through a fine mesh sieve if desired for an extra silky texture.

Transfer to a bowl, cover with plastic wrap directly on the surface, and chill completely before using.