1. Bring fruit, ginger, and water to a simmer in a large pot. Cook until fruit is soft, 10 to 15 minutes. Let cool slightly, then strain through a cheesecloth-lined sieve into a large saucepan, pressing on fruit. (Press gently to prevent syrup from becoming cloudy.) Discard fruit. Add sugar and taste, adding more as needed to reach desired sweetness.

2. Bring juice mixture to a gentle simmer, stirring often until sugar dissolves. Add mint, and cook over medium-high heat, stirring often, until liquid reduces to a light syrup, about 15 minutes. (You should have 8 cups.) Let cool completely. Discard mint. Transfer syrup to sterilized bottles or airtight containers. Cover, and refrigerate for up to 3 months.