Ginger Syrup: In a small saucepan, combine 1/2 cup sugar with 4 ounces water. Simmer over moderate heat, stirring, until the sugar dissolves. Add 1⁄3 cup (1 1/2 ounces) minced fresh ginger and simmer over very low heat for 30 minutes, stirring occasionally. Let cool, then pour the syrup through a fine strainer into a jar. Refrigerate for up to 2 weeks. Makes about 5 ounces.