In a bowl, rub the lime zest and granulated sugar together until the texture of wet sand forms, and all the granules have been rubbed together. This releases the lime oil into the sugar for more flavor.
In a saucepan, whisk together the zest and sugar mixture, fresh lime juice, and granulated sugar.
Bring to a simmer over medium heat until sugar is dissolved completely. Remove from heat and strain the zest and any pulp through a fine mesh sieve. If you want to remove even finer particles, use a cheesecloth.
Let cool and transfer to a glass jar or other airtight container and store in the fridge for up to 2-3 weeks.