Combine lime peel, lime juice, ginger, sugar, and 30 mint leaves in mortar or medium bowl. Using pestle, muddler, or handle of wooden spoon, crush lime peel, ginger, and mint leaves together. Transfer mixture to large pitcher. Stir in rum. DO AHEAD. Can be made 6 hours ahead. Cover and refrigerate.
Add 3 cups ice cubes to lime mixture in pitcher and stir to blend. Stir in ginger beer. Fill 10 cocktail glasses with ice cubes. Strain or pour cocktail mixture into prepared glasses. Garnish each drink with mint sprig.