Heat olive oil in a large pot over medium heat. Add the chopped onion and sauté for about 5 minutes until it becomes translucent. Stir in the minced garlic and cook for another minute until fragrant.
Toss in the chopped Roma tomatoes, allowing them to cook down for 10 minutes. Stir occasionally to break them apart.
Once the tomatoes have softened, add the 32-ounce carton of vegetable broth. Stir and bring the mixture to a boil, then reduce the heat and let it simmer for 20 minutes.
If you prefer a smoother soup, use an immersion blender directly in the pot, or carefully transfer the soup in batches to a regular blender. Blend until smooth.
Stir in the chopped fresh basil and let the soup simmer for an additional 5 minutes to allow the flavors to meld.
Add salt, pepper, and a bit of sugar if the soup tastes too acidic. Stir everything together and let it simmer for a final 5 minutes.
Ladle the soup into bowls and, if you like, garnish with fresh basil leaves and a sprinkle of Parmesan cheese.