In a large saucepan, combine the sugar, water, and grapefruit juice and stir over medium-high heat until the sugar is completely dissolved, 5 minutes. Gently bruise the ginger and rosemary with the back of a spoon to release some of their oils. Add them to the pot along with the grapefruit zest. Lower heat to medium and let cook for 5 minutes; do not boil. Remove from heat and let cool for 30 minutes. Cover and refrigerate overnight.
Divide the ginger slices, rosemary sprigs, and grapefruit peel evenly among five 6-ounce Mason jars and fill with the syrup.
Store in the refrigerator for up to 2 weeks.
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