Preheat the oven to 400ºF. Cut the tomatoes into quarters or halves, depending on the size of the tomatoes. Slice the onion into 1-inch wide wedges. Peel the garlic.
Place the tomatoes, onions, and garlic on a large sheet pan. Sprinkle with ¼ tsp salt and ⅛ tsp pepper, then drizzle with the olive oil. Toss to coat everything in oil.
Roast the vegetables in the oven for 40-45 minutes or until they become slightly browned on the edges.
Transfer the vegetables and all of the juices to a soup pot and purée with an immersion blender. Or, transfer to a blender, add the vegetable broth, and purée.
Add the basil and vegetable broth (if not already combined) to the soup pot and heat over medium. Allow the soup to come up to a simmer, then continue to simmer, stirring occasionally for 10 minutes.
After simmering for 10 minutes, add salt to taste. The total amount of salt needed with depend on the salt content of the broth used, so start with ¼ tsp and add more until the flavors are vibrant. Serve hot with a grilled cheese or garlic bread for dipping!