Place the halved tomatoes on a baking sheet, cut side up. Drizzle with olive oil and sprinkle with salt, pepper, dried basil, and oregano.
Cut the top off the head of garlic, drizzle with a little olive oil, and wrap it in aluminum foil. Place it on the baking sheet with the tomatoes.
Roast both the tomatoes and garlic in the preheated oven for about 30-35 minutes, or until the tomatoes are soft and slightly caramelized.
Remove the baking sheet from the oven and let cool for a few minutes. Squeeze the roasted garlic cloves out of their skins into a blender or pot.
Add the roasted tomatoes (and any juices from the baking sheet), chopped onion, vegetable broth, and balsamic vinegar to the blender.
Blend until smooth. If you prefer a chunkier texture, you can pulse it a few times to leave some pieces intact.
Transfer the mixture to a pot and heat over medium heat. Let it simmer for about 10 minutes to meld the flavors. Adjust seasoning with extra salt and pepper if needed.
Serve hot, garnished with fresh basil leaves, alongside crusty bread if desired.