Step 1: Make the syrup:
Step 2: Place the rosemary sprigs and 1/2 cup near-boiling water in a sealable heatproof container. Let steep 20 minutes. Add the honey and stir gently until dissolved. Cover and let steep another 2 hours minimum, but 12 hours preferably. Strain. Refrigerate.
Step 3: Make the Cocktail:
Step 4: Fill a cocktail shaker with ice. Add the gin (or rum), lime juice, and rosemary syrup. Shake until frosty, about 20 seconds. Strain into a coupe glass. Tap the rosemary sprig lightly against your hand to release the essential oils, then use it to garnish the glass.
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