Blanch tomatoes after cutting an "x" into the blossom end by dropping them into boiling water for a few seconds, then plunge them into cool water. When cool, remove skins, cut tomatoes in half across the equator, and squeeze out seeds, gel, and water while working over a fine stainer on top of a bowl to catch the liquid. Chop tomatoes roughly, and place into a large pot. Scrape the gel and seeds against the bottom of the strainer with a spoon or your fingers, then discard the seeds. Put all the liquid from the bowl into the pot. In a medium skillet, heat oil over medium heat until rippling in the pan. Add the onion and carrot and saute for 4 minutes or until the onions are transparent. Add the garlic and saute 30 seconds. Add the onion mixture to the tomatoes in the pot, then add the tomato paste, water, chicken base (or you can use chicken bouillon), and the chopped tomatoes, as well as the salt and pepper. Simmer for 15 minutes. Add the basil during the last five minutes. Remove from the heat, stir in the cream, adjust the seasonings as needed to taste. Allow to cool then blend into a smooth puree. Reheat and serve.