Spread the sugar in a shallow dish. Moisten the rim of a highball glass with water and dip the rim in the sugar to coat. Fill the glass with ice.
In a cocktail shaker, muddle the lemon wedges with the Lemon-Thyme Syrup. Add 1 cup of ice and the vodka and shake well. Strain the vodka mixture into the highball glass and top with club soda. Garnish with the thyme sprig and serve.
The Lemon-Thyme Syrup can be refrigerated for up to 5 days.
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