Preheat oven to 400 degrees. Line a baking sheet with foil and spread the tomatoes in an even layer. Sprinkle with olive oil, salt, pepper, and vinegar. Roast for about 30 to 35 minutes or just until the tomatoes begin to char a little.
Transfer the roasted tomatoes to a blender in small batches and blend until smooth. Add water as needed to the tomatoes if the mixture is too thick to blend. Pour the blended tomatoes into a large soup pot.
On medium-low heat, add the vegetable broth, milk, and honey to the blended tomatoes in the soup pot. Stirring often, bring the mixture to a simmer. Simmer for 10 minutes. Ladle into serving bowls and sprinkle basil on top.
If desired, sprinkle with a tablespoon of parmesan cheese. Find the recipe below.