Muddle the cilantro with the lime juice and the Cilantro Simple Syrup in a cocktail shaker. Add 1 cup ice and top with the rum. Cover and shake well. Then pour into a tall thin glass without straining (like a Collins glass). Top with a splash of club soda and garnish with the lime wedge on the rim of the glass.
Combine the sugar with 1 cup water in a small saucepan, and bring to a simmer over medium-high heat. Once simmering, stir until the sugar dissolves, then remove from the heat. Add the cilantro stems and allow the flavors to infuse and the mixture to cool, at least 15 minutes. Strain out the stems and then store the syrup in the refrigerator.
From Food Network Kitchens