Preheat your oven to 400 degrees Fahrenheit.

On a large sheet pan, spread out your halved tomatoes and quartered onions. Place the garlic heads on a piece of foil, drizzle with oil, and wrap them tightly. Drizzle the rest of the vegetables with olive oil and sprinkle with salt, pepper, and dried herbs.

Roast in the oven for about 40 to 45 minutes. You want the tomatoes to be shriveled and the onions to have dark brown edges.

Carefully open the garlic foil. Once cool enough to touch, squeeze the soft, roasted cloves out of their skins. They should be the consistency of soft butter.

Transfer the roasted tomatoes, onions, and garlic into a large pot. Add the vegetable or chicken broth. Bring the mixture to a gentle simmer for about 10 minutes to let the flavors blend.

Use an immersion blender directly in the pot, or transfer safely to a stand blender. Blend until completely smooth and velvety.

Stir in the heavy cream and fresh basil. Taste and adjust your seasoning. If the soup is too thick, add a splash more broth until you reach your desired consistency.