Add the tomato paste, Italian seasoning, and sugar and stir to combine. Add the tomatoes (with the liquid) and the vegetable stock and stir. Bring the soup to a boil, reduce heat to low, and simmer, covered, for 15 minutes.
Make it smooth:
With an immersion blender: insert it directly inside the soup pot and blend continuously and around the pot for 2 minutes or until the soup is smooth. With a traditional blender: laddle some of the soup into the blender jar, filling it no higher than halfway, and working in batches, blend it until smooth. Transfer the blended soup to a large bowl and blend the rest. Once it's creamy and smooth, combine the batches back into the pot.
Bring the blended veggie tomato soup back to a boil and simmer it, uncovered, for 5 more minutes. If you want a thicker soup, simmer it longer to evaporate some of the excess liquid.
Ladle the veggie soup into bowls and enjoy with sliced crusty bread or a grilled cheese sandwich.