Make the tomato base: In a high powered blender such as a Vitamix, blend the tomatoes, onion, spices, olive brine and Worcestershire sauce with tomato juice until very smooth.

Add the horseradish to the blender and continue blending until the pieces of horseradish are very small, fine enough to drink through a straw.

Pour the mixture into a large container. Add the chopped capers to the container and stir thoroughly to combine.

Add the hot sauce and mix. Taste and season with more salt if needed. Refrigerate until ready to use.

Make the cocktail: Combine the vodka, lemon juice, and bloody tomato base in a shaker. You may need to do this in two batches, to accommodate the size of the shaker. Shake well, divide between 4 Collins glasses and garnish with fresh black pepper. Serve on the rocks.