Washing and chop the tomatoes, pepper, and onion. Make sure you are using the best quality fruits and vegetables possible-- gazpacho is a raw dish.
Blend the tomatoes, green pepper, onion, and garlic until completely pureed.
Strain the blended vegetable juice through a fine mesh strainer.
Everything should pass through except for a layer of seeds and skin. Discard this.
Add the vegetable juice back to the blender and add the watermelon. Blend again until completely pureed.
Add salt to taste (go easy, you can always add more later), and a couple splashes of vinegar and blend. Everyone has a different preference on how much vinegar to add, so my advice is to start with a teaspoon or two and adjust at the end.
Finally, slowly add in the extra virgin olive oil (better olive oil means better gazpacho) as the blender is running.
Taste the gazpacho for salt and vinegar and adjust if necessary. Then, add two to four ice cubes (depending on how thin you like your gazpacho). Let them melt for a few minutes in the blender and then add a handful of fresh mint and blend for the last time.
Taste for salt and serve ice cold in glasses. If you insist on serving in a bowl you can top with diced watermelon or diced red bell pepper.