Mix or whisk egg yolk, egg, and ½ cup sugar in a heavy bottomed saucepan until light and pale.
Add lime juice and lime zest.
Stirring constantly, cook over medium heat until thick and bubbling, about 5-7 minutes.
It should be thick enough to coat the back of a spoon
Remove from heat and stir in butter one tablespoon at a time
While still warm, strain through a mesh sieve
Let cool and then cover and refrigerate until ready to use
This lasts up to a week in the fridge or up to 3 months in the freezer