Mix the tomatoes with the herbs, sugar, seasoning and half the olive oil in a bowl. Crush everything with your hands until the mixture is a pulp, then puree in a blender until very smooth. It is best to do this in 2 batches, filling the blender half full each time. Pass the mixture through a fine sieve, pressing down well with the back of a spoon to extract all the flavour from the tomatoes.
Put half the gazpacho in a blender with half the remaining oil and blend for 45 seconds. Repeat with the remaining soup and oil. Place the gazpacho in the fridge to chill while you make the basil oil.
First pick all the basil leaves off the stems. Bring a pan of water to the boil, add the leaved and cook until they are just soft but still have a little bite (45-60seconds). Drain the leaves immediately and place them in iced water for a minute until they are completely cold.
Drain the basil leaves again, squeezing out all the water. Place the basil in a blender with the olive oil and blend on a high speed for 15 seconds until you have a puree. Pour it into a bowl set over iced water so it cools instantly.
To finish the soup halve the cherry tomatoes for the garnish and mix them with a little of the basil oil. Place a spoonful of this in the bottom of each bowl, then top up with soup and add a little more basil.