Gazpacho Bloody Marys

Name: Gazpacho Bloody Marys
Cuisine: European, Mediterranean
Ingredients: 2 28-ounce cans Italian tomatoes (such as San Marzano) with juice; 1 English hothouse cucumber, peeled, chopped (about 2 cups); 1/2 cup fresh lemon juice; 2 tablespoons fresh cilantro leaves; 4 teaspoons prepared horseradish; 4 teaspoons Worcestershire sauce; 2 teaspoons celery salt; 12 dashes of hot pepper sauce; Ice cubes; 2 cups vodka; 1 English hothouse cucumber, halved crosswise, then quartered lengthwise