The Tom and Ginger Cocktail

Name: The Tom and Ginger Cocktail
Ingredients: Spicy Heirloom Tomato Juice; 2 cups very ripe tomatoes, preferably heirloom, chopped; 1 teaspoon grated fresh garlic; 1 teaspoon slivered fresh chile pepper (I used serrano); 2 tablespoons minced red onion; 2 tablespoons finely chopped fresh cilantro; 1 teaspoon kosher or sea salt; 1/4 teaspoon freshly squeezed lime juice; Tom and Ginger; 2 ounces vodka; 3/4 ounce Spicy Heirloom Tomato Juice; 1/4 ounce bianco vermouth; 1/4 ounce freshly squeezed lime juice; 1 teaspoon Canton ginger liqueur; 2 dashes lemon bitters; (optional) cherry, grape or pear tomato half, for garnish