Position a rack in the middle of the oven and preheat to 350 degrees . Line 2 baking sheets with parchment paper or a silicone baking liner. Sprinkle four 1/4-cup mounds of parmesan about 2 inches apart onto each prepared baking sheet; slightly flatten with a spoon. Bake until golden-brown, 6 to 8 minutes. Let cool for 30 seconds. Using a thin metal spatula, drape the crisps over a rolling pin until hardened into shape, about 3 minutes.
In a soup pot, heat the olive oil over medium heat. Add the onion and carrot and cook, stirring, until softened, 5 to 7 minutes. Add the vegetable broth and tomatoes, cover, and bring to a boil.
Using a blender, puree the soup with the butter. In the soup pot, stir the pasta into the soup,and cook until al dente, Stir in 1 to 2 cups water, if desired. Season with salt and pepper.
Ladle the soup into 4 mugs and top each with 2 parmesan crisps. The parmesan crisps can be kept in an airtight container for up to 2 days.