Crush the canned tomatoes with a fork in a bowl. Then press everything through a fine sieve so that only the tomato juice remains.
Peel and quarter the shallots. Peel the garlic. Halve the cherry tomatoes.
Steam in a pan, olive oil, shallots and garlic at low heat for 5 minutes until translucent. Then add the cherry tomatoes, salt and sugar. Cook for another 5 minutes, stirring occasionally. Then remove the garlic from the pot. Add the tomato juice and simmer with the lid closed for 20 minutes.
Stir in basil and cook for 5 minutes.
Puree everything with a hand blender. Season with salt and pepper.