In a blender or small food processor combine tomatoes and the large basil leaves. Cover and blend or process until smooth. Chill for 30 to 60 minutes. Place a fine-mesh sieve over a bowl and strain the mixture through the sieve, using a spatula to press the liquid through (you should have about 1 cup strained liquid, depending on the tomatoes). Discard the pulp in the sieve.
Add a few ice cubes to a cocktail shaker; pour the strained liquid into the shaker. Add vodka, Worcestershire sauce, hot pepper sauce, salt, celery salt, and black pepper to the shaker. Cover shaker; shake vigorously until mixture is chilled. Strain into two ice-filled glasses. Garnish with small basil leaves and, if desired, cucumber spears.