Your Gazpacho can include any number of ingredients - avocado, cucumber, watermelon, grapes, even seafood. Modern recipes will often include sugar to counter the vinegar as a gastrique - paleo, we can simply leave that out and enjoy the genuine article.
Let's start out simple ...
First, the tomatoes - simply quarter and place into a bowl and then pound with the end of a rolling pin until a pulp is achieved, stopping short of a puree. You could use a food processor or blender, but mashing is more fun!
Add a good glug of extra virgin olive oil or avocado oil, a splash of cider vinegar and any other ingredients you want to include - diced cucumber, avocado, whatever. I like to use pickled chillis for a lighter vinegar flavour, a good tang and a little bite.
Pure sea salt to taste and a grind of pepper.
Finally, a little chilled water or even crushed ice cubes just to cool the dish.