To make hibiscus syrup: Bring 2 cups water, 1/2 cup white sugar, 1/3 cup hibiscus flowers, 1/4 cup brown sugar, a 1/2-inch piece of fresh ginger, and the zest of 1 lemon to a boil in a small saucepan. Reduce heat and simmer until sugars dissolve, about 10 minutes. Remove from heat and let mixture steep, about 5 minutes. Strain through a fine-mesh strainer, pressing mixture to extract as much liquid as possible. Discard solids and store syrup in the refrigerator for up to 2 weeks.