1Wrap 1 of the basil leaves around mozzarella ball. Thread mozzarella and cherry tomato on cocktail pick or skewer; set aside for garnish.
2Add vodka and remaining 3 basil leaves to cocktail shaker; use muddler or wooden spoon to muddle basil, releasing its flavor into vodka.
3Add tomato juice, salt and enough ice to fill shaker; shake until well chilled. Pour into ice-filled glass (discard basil from shaker). Add garnish.