Preheat the oven to 400°F.
Cover a rimmed baking sheet with parchment paper. Arrange the quartered tomatoes across the pan and scatter the unpeeled garlic cloves among them.
Pour the olive oil over the tomatoes and garlic. With clean hands, gently coat everything in the oil and spread the ingredients evenly over the baking sheet. Season with the salt and cracked black pepper.
Place the baking sheet in the oven and roast for 1 hour, until the tomatoes are extremely tender and beginning to caramelize along their edges.
When approximately 30 minutes of roasting time remain, begin preparing the onion mixture. Place a Dutch oven over medium heat. Add 1 tablespoon olive oil and allow it to heat until shimmering.
Add the diced onion and cook, stirring from time to time, until softened, about 6–7 minutes.
Stir in the dried basil and oregano. Continue cooking for 1–2 minutes, just until the herbs become aromatic.
Pour in the balsamic vinegar to deglaze the pot. Let it cook until the bubbling subsides and the vinegar has reduced by half.
Add the vegetable broth and fresh thyme. Increase the heat to high and bring the liquid to a boil. Lower the heat to medium-low and simmer for 10–15 minutes so the thyme and seasonings can flavor the broth. Turn off the heat.
Once the tomatoes have finished roasting, use tongs to remove the hot garlic cloves from the baking sheet. Set them aside for about 5 minutes, or until they are cool enough to handle safely.
Remove the thyme sprig from the broth, giving it a shake over the pot to release any leaves.
Transfer the roasted tomatoes into the Dutch oven with the broth and onions. Squeeze each softened roasted garlic clove from its papery skin and add the garlic to the pot.
Add the ¼ cup heavy cream, if using, along with ¼ cup fresh basil. Blend directly in the pot with an immersion blender until the soup is smooth. If the soup is thicker than you prefer, add additional broth until it reaches your desired consistency.
Spoon the hot soup into bowls and finish with additional fresh basil. Serve immediately. Refrigerate leftover soup in a tightly sealed container for up to 1 week, or freeze it in an airtight container for up to 3 months.