Yellow cherry tomatoes, halved, and basil flowers, for garnish
In a jar, cover the jalapeños with the vodka. Let stand for 3 hours, then strain.
In a food processor, puree the tomatoes. Pass the puree through a fine sieve into a large measuring cup; you should have 2 cups of juice. Pour it into ice cube trays and freeze until firm, about 3 hours.
In a blender, combine the jalapeño vodka, tomato ice cubes and basil. Blend until smooth and season with salt; if the drink is very thick, add a little water and blend again. Pour into rocks glasses, garnish with cherry tomato halves and basil flowers and serve.