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Makes 8-10 drinks
30 minutes preparation time, plus several hours for chilling
2 cups granulated sugar
2 cups water
4 Granny Smith apples, plus extra slices for garnish
1/2 cup fresh squeezed lime juice (from about 6 limes)
2-3 quarts seltzer water
Put the sugar and water in a small saucepan over medium heat. Bring the mixture to a low boil and stir until the sugar dissolves. Remove the pan from the heat and set it aside to cool.
Cut the apples into quarters and remove the cores. Grate or shred the apples (I used a food processor, but you could also use a grater). Pour the shredded apples into a large pitcher (or two, if you don't have one large enough). Add the lime juice and, when the syrup has cooled to room temperature, add it too.
Let the mixture sit for several hours or overnight to allow the flavor of the apples to steep into the sugar syrup. Before serving, pour through a strainer into another pitcher, mashing the shredded apples with a back of the spoon against the strainer to remove all of the juice.
To serve, fill a 12-ounce glass with ice. Add about 1/3 cup syrup and top off the glass with seltzer. Stir. Taste and add more syrup, if you want a stronger flavor. Garnish with a slice of apple.