Beetnik Martini

Directions

1. 1
   Cook beets in a large saucepan of boiling water until tender, 1-1 1/4 hours. Drain; let cool slightly. Peel and slice. Combine warm beets and vodka in a large 1 1/2-quart jar (save vodka bottle to store finished product). Cover; chill for at least 5 days and up to 1 week. Strain into a medium bowl; discard beets. Pour beet vodka back into reserved bottle. Cover and chill.
2. 2
   Bring sugar, ginger, and 3/4 cup water to a boil in a small saucepan, stirring to dissolve sugar. Let cool. Strain ginger syrup into a medium jar; discard ginger. Cover and chill. DO AHEAD:
3. 3
   For each cocktail, combine 2 ounces beet vodka, 1/2 ounces ginger syrup, 1/4 ounce lemon juice, and 1/4 ounce lime juice in a cocktail shaker filled with ice. Shake vigorously until cocktail shaker is very cold. Strain drink into a coupe or Martini glass. Float a lemon slice on top.