Add all the gazpacho ingredients to a high-speed blender (for a smooth gazpacho) or food processor (for more texture). Blend or process on low and then increase to high and blend until your desired texture is reached.
Next, I like to strain the gazpacho using a sieve or fine mesh strainer so the gazpacho is silky smooth. Set up a fine mesh sieve/strainer over a large bowl. Pour the gazpacho, a little at a time, through the sieve and use a large spoon or spatula to pass the gazpacho through the sieve. This will take a few minutes. Discard the pulp or add it to your next stock or soup recipe.
Taste and reseason as needed with salt, pepper, or vinegar (if you like a tangier flavor), then transfer the strained gazpacho to the fridge and let chill for a couple of hours.
To serve, divide among glasses or small bowls and garnish as you wish! If you want to thin the gazpacho, simply stir in a little cold water.