Time: About 20 minutes, plus infusing time.
In a medium saucepan, heat sugar with 1/2 cup water, stirring, until sugar is dissolved. Let cool to room temperature.
Stir in vodka. Pour mixture into a decanter and add kumquats (halves first) and thyme. Chill at least 3 weeks. Serve ice-cold, in shot glasses.
Note: Nutritional analysis is per 2-oz. serving.
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