Combine thyme and vodka in a clean glass jar or bottle. Cover and let stand in a cool, dark place for 6 weeks, giving the mixture a shake every few days
Combine sugar and water in a small saucepan. Boil until sugar has completely
dissolved. Let cool.
Strain vodka mixture through a coffee filter into a clean jar or bottle with
an airtight lid. Sweeten to taste with the sugar syrup. Add fresh thyme as a
garnish in the bottle or jar, if desired. Cover and age at least 2 weeks.
Store in a cool, dark place for up to 1 year.