How to Make It
Combine first 3 ingredients in a saucepan over high heat. Bring to a boil, stirring until sugar dissolves. Remove from heat; let stand 15 minutes. Strain; discard solids.
To prepare each cocktail, muddle 3 mint leaves and 1 rind strip in a cocktail shaker using the handle of a wooden spoon. Add 2 1/2 tablespoons ginger syrup and 1/2 cup orange juice to shaker; shake well. Pour mixture into an ice-filled glass. Top with 1/2 cup soda; stir. Garnish with an orange wedge and a mint sprig.