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Crush 8 oz. ginger, scrubbed, coarsely chopped, with a mortar and pestle or finely chop. Combine ginger, ¾ cup sugar, ¾ tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and ¾ cup water in a medium skillet and bring to a boil. Cook, stirring occasionally, until sugar is dissolved and syrup is slightly reduced, about 3 minutes. Remove from heat and let sit 15 minutes.
Strain syrup through a fine-mesh sieve into a heatproof measuring glass; discard solids. Stir in ¼ cup fresh lime juice.
Divide mixture among four 8–10-oz. glasses. Add ice, then top off each glass with about 6 oz. sparkling water. Garnish with lime wedges or wheels.
Enjoy!
