Soak the gelatin sheets in cold water for about ten minutes.
In the meantime, blend the tomato puree in the mixer with the peeled and sliced cucumber, the bell pepper with seeds removed and cut into pieces, the peeled onion and the garlic.
Season with vinegar, salt and pepper.
Heat 5 or 6 tablespoons of gazpacho in a saucepan and dissolve the soaked and squeezed gelatin.
Mix with the rest of the blended vegetables, add the basil leaves torn into small pieces and pour into 6 small glasses or in a dish with edges at least 3 centimeters high.
Store in the fridge for at least a couple of hours.