Combine the syrup ingredients in a small saucepan. Bring to a boil and boil for 5 minutes, stirring until the sugar dissolves. Remove from heat and strain the mint leaves. Allow to cool at room temperature or place in the refrigerator. The syrup can be made a few days ahead of time.

When ready to serve, place the chopped mint leaves in the bottom of the serving pitcher. Add the syrup, freshly squeezed lime juice, and 8 cups of cold water. Taste and add additional water to taste (if necessary). If serving over ice, you might want to make it a tiny bit sweeter than you would normally like to account for the dilution from the melted ice.

To make the lime sugar for the rims of the glasses, mix the zest of one lime with 1/2 cup sugar. Using a damp paper towel, wipe around the rim of each glass and then invert the glass into the lime sugar. Carefully fill the sugar-rimmed glasses with ice cubes and pour the limeade into the glasses to serve.