Heat the oven to 400°F.
Line a rimmed baking sheet with parchment. Spread the tomatoes on it and scatter the garlic cloves throughout.
Drizzle the tomatoes and garlic with olive oil, rub to coat, season with salt and pepper, and roast for 1 hour until soft and caramelized at the edges.
When 30 minutes remain, heat 1 tablespoon olive oil in a Dutch oven. Sauté the onion 6–7 minutes, then add basil and oregano for 1–2 minutes.
Add balsamic vinegar and reduce by half. Add broth and thyme, bring to a boil, then simmer 10–15 minutes.
Cool the roasted garlic enough to handle, then squeeze it from its skins.
Remove the thyme, add roasted tomatoes and garlic to the broth, and add cream and fresh basil.
Blend with an immersion blender until smooth, adding broth if needed.
Ladle into bowls and garnish with basil. Serve immediately.