Add olive oil to a Dutch oven or a large pot over medium-high heat. Add in onion and saute for 5-7 minutes until softened. Add the garlic and saute 1-2 minutes longer. Add in the crushed and fire roasted tomatoes along with sugar, salt, pepper, broth, bay leaf, and thyme. Allow to come to a simmer and reduce heat to medium-low. 

Alternatively, ladle the soup into a food processor or blender, a couple cups at a time, and pulse. Take care not to let steam build up in either machine. This can be accomplished by removing the tube feed from either device and covering instead with a dish towel while pulsing.

Place the pulsed soup into a large mixing bowl until all of the soup has been processed. Return soup to the Dutch oven. Stir in the basil and cream and allow to simmer 10 minutes more. Remove from the heat, garnish with basil, serve and enjoy