Preheat oven to 450*
Toss tomatoes, carrots, onion and garlic with olive oil and spread in an even layer on a baking sheet. Roast for 20-25 minutes or until veggies start to char and carrots are fork tender.
Transfer all the veggies and garlic to a stockpot with 2 cups of broth, butter, parmesan cheese rind and bay leaves. Be sure to remove the skins from the garlic if you roasted in the skin.
Bring to a boil and then simmer, uncovered for 20 minutes. Remove cheese rind and bay leaves.
Using an immersion blender, puree soup until smooth*
If needed, slowly add more broth until desired consistency is reached. Turn off the heat and stir in half and half and parmesan cheese. Serve hot.
*if you do not have an immmersion blender, you can also puree the soup in a regular blender and then continue to finish the soup on the stove. If you choose this method, be sure to use a thermal control blender or allow the soup to cool before blending. Always be sure to consult your blender's instructions for pureeing soups or hot liquids.