Arrange the quartered tomatoes on a baking sheet. Cut the top off the head of garlic to expose the cloves and place it on the baking sheet with the tomatoes.
Drizzle the tomatoes and garlic with 1 tablespoon of olive oil, season with salt, pepper, and sprinkle dried basil and oregano.
Roast everything in the oven for 25-30 minutes, until the tomatoes are soft and the garlic is golden and fragrant.
While the tomatoes and garlic roast, heat the remaining tablespoon of olive oil in a large pot over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Once the tomatoes and garlic are done roasting, remove them from the oven. Squeeze the roasted garlic cloves out of their skins and add them to the pot with the sautéed onions.
Add the roasted tomatoes and any juices from the baking sheet into the pot. Pour in the vegetable broth and bring to a simmer. Let it cook for about 10 minutes.
Use an immersion blender to puree the soup until smooth. If you prefer a chunky texture, just blend until you achieve your desired consistency.
Stir in the balsamic vinegar and, if desired, heavy cream for extra creaminess. Heat through for another few minutes.
Taste and adjust seasoning if needed.
Serve hot, garnished with fresh basil leaves.
Notes
For a creamier texture, add heavy cream to the soup.