Preheat oven to 400 degrees. Place prepare a baking sheet with a piece of parchment paper and place tomato halves on sheet, skin side down with garlic cloves. Drizzle with olive oil, toss with your hands and coat with kosher salt and pepper. Roast in oven for 15 minutes. Remove from oven. Discard herbs and remove paper from garlic and set aside.
In a large stock pot melt 2 tablespoons butter over medium heat. Add carrot and onion, season with kosher salt and sauté for 5 minutes or until onions become translucent, about 4 minutes. Add tomatoes and reserved garlic and stir to combine. Add vegetable stock and V-8 juice and bring to a boil then reduce to simmer. Cook for 20-25 minutes until reduced by half and tomatoes are soft. Remove from heat and blend with an immersion blender until smooth. Add half and half or cream, orzo and slivered basil and cook for another 5 minutes. Add parmesan and garnish with additional basil.