Preheat oven to 375 degrees and line a baking sheet with parchment paper.
Chop up Roma tomatoes and cut cherry tomatoes in half if desired. Arrange all vegetables (tomatoes, onions and carrots) on baking sheet and garlic cut side down. Add on rosemary sprigs. Drizzle with olive oil and season with salt, pepper and Italian seasoning. Roast in the oven for about 55 minutes to one hour. Remove from oven and let cool slightly until cool enough to handle the garlic, about 5 minutes.
Using your Dutch oven or large pot, heat about 2 tablespoons of olive oil. After a few minutes, add the tomato paste and cook, stirring constantly, until it darkens slightly in color, about 2 minutes.
Squeeze the garlic cloves out of the garlic head onto the baking sheet and discard the peels. Also, remove the rosemary sprigs and discard. Add all of the roasted tomato mixture, including any juices and the roasted garlic into your pot. Cook until the tomato paste is fully mixed into the tomato mixture, for about 2 to 3 minutes.
Add 3 cups low-sodium vegetable broth and season with the sugar and 1/2 teaspoon kosher salt. Bring to a boil. Reduce the heat as needed and let simmer for about 5 minutes to let the flavors meld. Turn off the heat. Blend directly in the pot with an immersion blender until smooth, OR transfer in two batches to a high speed blender and blend until smooth. For this soup, if you have a blender, I recommend using your blender to get a smoother and creamy soup.
Taste and season with more kosher salt as needed. Garnish with fresh basil leaves if desired. Enjoy! highly recommend enjoying this soup with a grilled cheese sandwich!