Preheat your oven to 400°F (200°C). Arrange the halved tomatoes, onions, and bell peppers on a large baking sheet. Cut the top off the garlic head to expose the cloves, drizzle with a little oil, wrap it tightly in foil, and place it on the tray. Drizzle the remaining olive oil over the vegetables and season with salt, pepper, and oregano.
Roast the vegetables in the oven for 40 to 45 minutes. You are looking for the tomatoes to be soft and the skins to have a bit of a char. The garlic should be completely soft and golden brown inside its foil pouch. This roasting process is where all the deep flavor is created.
Once the tray has cooled slightly, squeeze the roasted garlic cloves out of their skins directly into a large pot or a high-speed blender. Add the roasted tomatoes, onions, peppers, and any flavorful juices left on the baking tray into the pot.
Add the fresh basil and vegetable broth to the mixture. Use an immersion blender to blend the soup until it is completely smooth. If you prefer a thinner consistency, add a little more broth. Transfer to a stovetop over medium heat and stir in the heavy cream if you are using it. Simmer for 5 to 10 minutes to let the flavors meld together perfectly.