Step 1

Combine sugar and water in a small saucepan. Cook, stirring, over low heat until sugar dissolves, then add fresh thyme for syrup. Simmer gently, covered, for 30 minutes. Strain syrup into a glass measuring cup, leaving a few leaves in it. Set cup with syrup in a small bowl of ice water to cool, or just set aside if you don’t need it right away. If making thyme syrup ahead, chill airtight up to 1 week.

Step 2

Meanwhile, discard seeds and peel from cantaloupe and cut melon into chunks. Puree melon in a blender until very smooth, then strain, or juice it in a juicer. If making melon puree ahead, refrigerate up to 3 days and stir before using.

Step 3

For each cocktail, put sherry, gin, .75 ounce thyme syrup, lemon juice, 1 ounce melon puree, the salt, and ice cubes in a cocktail shaker. Shake vigorously until shaker is cold. Then strain into a small cocktail glass (preferably a coupe style); or for a more casual look, just pour everything including ice into a glass. Set a thyme sprig over the glass, or if you like, spear a couple of melon balls with a thyme sprig or skewer and set them on the glass.