1. Position a rack in the middle of the oven and preheat to 350°. Line 2 baking sheets with parchment paper or a silicone baking liner.
2. 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.
3. Using a thin metal spatula, drape the crisps over a rolling pin until hardened into shape, about 3 minutes.
4. 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.
5. Using a blender, puree the soup with the butter.
6. 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.
7. 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.

Serves 4.