In a small saucepan over medium-high heat, bring 1/2 cup sugar, 1/2 cup water, and 2 Tbsp. grated fresh ginger to a boil. Reduce heat to maintain a simmer and cook until slightly thickened, about 10 minutes. Transfer syrup to a small metal bowl and let sit until cool, about 10 minutes. Strain (discard the ginger) and use warm, let cool to room temperature, or store, covered and chilled, up to six months.