In a large pot, heat the olive oil over medium heat. Add the onions and carrots then sauté for 5-10 minutes until softened and fragrant, stirring occasionally.
Stir in the dried basil, salt, and pepper, canned tomatoes (with their juice), and veggie stock. Bring to a simmer and cook uncovered for 20-25 minutes, until the flavors meld together.
Turn off the stove, add the fresh basil, then use an immersion blender (or a high-speed blender in batches) to purée the soup until silky and smooth.
Return the soup to the pot over low heat. Stir in the heavy cream. Let it warm through gently but do not boil. Taste and adjust salt and pepper as needed.
Garnish with chopped basil, a drizzle of cream or olive oil to finish.