In a medium saucepan, combine granulated sugar and lime zest. Mix them together until the sugar is moistened and fragrant.

Add fresh lime juice and eggs to the saucepan. Whisk until well combined.

Cook the mixture over medium-low heat, stirring constantly, until the mixture thickens and coats the back of a spoon, about 10 minutes.

Remove the saucepan from heat. Add the butter pieces, one at a time, stirring until each piece melts before adding the next.

Strain the lime curd through a fine mesh sieve into a bowl to remove any cooked egg bits and ensure a smooth texture.