Add all the syrup ingredients to a small sauce pan. Bring to a simmer over medium-low heat. Reduce heat to low and simmer, stirring occasionally, for about 15-20 minutes, or until reduced by about half.
Strain the liquid through a fine mesh strainer. Allow the syrup to cool.
Notes
Storing the syrup: Cool to room temperature, then transfer to a glass container with a lid (a mason jar is great for this). Cover and store in the refrigerator for up to 2 weeks.To make a cold ginger drink: Fill a glass halfway with ice. Add 8 ounces of seltzer, lemonade, iced tea, or alcohol of choice to the glass. Stir in 2 tablespoons of ginger syrup. Garnish with a slice of lemon.To make hot ginger tea: Stir 3 tablespoons ginger syrup into a mug filled with with 8 oz. hot water. Garnish with a slice of lemon.