Special equipment: A juicer
Pass the beets through a juicer according to the manufacturer's directions. Pour the beet juice, gin, lemon juice and Simple Syrup into a shaker two-thirds full of ice cubes. Shake well. Strain into a tall, chilled cocktail glass. Top off with the club soda and garnish with the lemon peel.
Combine the sugar and 1 cup water in a small saucepan and heat over medium heat until the sugar is dissolved. Let cool. The syrup will keep for 2 weeks in the refrigerator.