Harvest your southernwood. Only use the green parts, not the stem, it's easy to pinch the leaves off. Give it a quick wash and pat it dry.
In a large pot, heat the sugar, lime juice, and water.
Once the sugar has dissolved, add the southernwood. Let it simmer for about 20 minutes with the lid on.
Once the southernwood has lost most of its color, set the pot aside and just let the mixture cool off for an hour.
Pour the syrup through a strainer to remove the southernwood leaves.
Fill the syrup into a clean glass jar and keep it in the fridge for 1-2 weeks. Mix it with sparkling water and enjoy. I usually mix 1 cup of sparkling water with 1 tablespoon of syrup, but you can add more or less for your preferred sweetness and intensity.