Cut the tomatoes into pieces and puree them in a food processor. Strain the pruee through a food mill fitted with the fine-mesh screen (this should yield about 5 cups).

Pour the puree into a saucepan. Add the thyme leaves, Tabasco, pepper, salt, oil, and vinegar and bring to a boil. Boil for 30 seconds. Then stir in 1 cup heavy cream and heat through.

Divide the soup among six soup plates, sprinkle with 1/2 cup shredded basil, and serve.