Combine the chopped tomatoes and fresh basil leaves in a high-speed blender.
Blend on high for 1-2 minutes, or until the mixture is completely smooth and liquid.
Pour the tomato-basil mixture into an airtight container and place it in the refrigerator to chill for at least one hour.
Once chilled, pour the mixture through a fine-mesh sieve set over a bowl or pitcher to remove any seeds or skin, ensuring a silky-smooth texture.
Discard the solids.
Fill a cocktail shaker with ice.
Add the strained tomato juice, pepper vodka, Worcestershire sauce, and hot pepper sauce.
Secure the lid and shake vigorously for 15-20 seconds until the outside of the shaker is well-chilled.
Strain the cocktail into a chilled glass filled with fresh ice and enjoy immediately!
Taste the final mix before serving. You can easily adjust the spice and savory notes by adding a pinch of celery salt or a squeeze of fresh lime juice.
