In a big soup pot, pour in the olive oil with the stove heat set to low.
Add the onions and carrots to saute until soft, about 5 minutes.
Add the minced garlic and saute for one more minute.
For the tomatoes, I blanch them, let them cool, then remove the peels and stem/cores.
Place the peeled tomatoes into a food mill (on top of a medium/large bowl to catch the juice) and turn them around until all of the seeds remain inside the mill and all of the tomato puree comes out into a bowl.
(I do this for about half of my tomatoes because it is so tiring; the seeds don't damage the flavor).
Pour all of the tomato puree and juice into the big soup pot.
Add the basil, sugar, salt and pepper, and chicken broth. Stir.
Cook on very low (with a sheet pan underneath the pot to prevent burning), for about 45 minutes.
Taste and add whatever you prefer.
Add the cream and heat up if you prefer cream of tomato soup.