Heat olive oil in a large saucepan or Dutch oven over medium-high heat.
Sauté onion and bell pepper until onion started to become translucent.
Add garlic and sauté for another minute.
Added diced tomatoes, tomato sauce, seasoning packets, and water. Bring to a boil, then reduced to a simmer and cook for 20 minutes.
Remove from heat. With a ladle or large spoon, scoop some of the vegetable solids and broth into a blender. Purée to desired smoothness. (How much of the solids you purée and for how long depends on how smooth or chunky you'd like the finished soup.)
Returned the purée to the soup pot. Add half and half. Return to burner on medium heat until mixture begins to return to a simmer.
Remove from heat. Stir in basil and serve immediately.