Step 1: In a large Dutch oven or heavy-bottomed pot, heat the olive oil over medium heat. Add the chopped onion and carrots. Sauté for 8-10 minutes, or until the onions are softened and translucent, and the carrots are slightly tender.
Step 2: Stir in the minced garlic and cook for another minute until fragrant. Add the tomato paste and cook, stirring constantly, for 2-3 minutes, allowing it to deepen in color and flavor.
Step 3: Pour in the crushed San Marzano tomatoes, vegetable broth, and balsamic vinegar. Add half of the fresh basil leaves (about 1/4 cup), bay leaf, sugar, salt, and black pepper. Bring the mixture to a simmer, then reduce the heat to low, cover, and let it cook for at least 20-25 minutes, allowing all the flavors to meld.
Step 4: Carefully remove the bay leaf. Using an immersion blender, blend the soup directly in the pot until it is completely smooth. Alternatively, carefully transfer the soup in batches to a regular blender and blend until silky smooth, then return to the pot.
Step 5: Stir in the heavy cream and the remaining fresh basil. Heat gently for another 5 minutes, without boiling, just until the cream is warmed through and incorporated. Taste and adjust seasonings as needed, adding more salt, pepper, or sugar if desired.
Step 6: Ladle the hot creamy tomato soup into bowls. Garnish with a swirl of extra cream, a few fresh basil leaves, and a crack of black pepper. Serve immediately with your favorite accompaniments, like a classic grilled cheese sandwich or crusty bread. For additional cozy meals, consider exploring our ultimate creamy tomato soup collection.