- In a medium saucepan, bring syrup ingredients to a boil.
- Turn down to a simmer, stirring often until mixture thickens and the sugar has melted.
- Cook for 20 minutes on low heat.
- Remove from heat and strain through a fine-mesh sieve into a medium bowl; discard solids.
- Let cool completely. Syrup can be stored, covered, in refrigerator up to 2 weeks.
- Pour all ingredients into a cocktail shaker.
- Shake and strain over a large ice cube into a cocktail glass and garnish with a sprig of thyme.