Choose small, sweet pumpkins for this soup. Peel pumpkin, and cut the flesh into small cubes. Peel onions and chop coarsley. Place pumpkin and onion in a soup pot with the garlic, sage, oil, and water. Season to taste with salt and pepper, then let simmer on low heat for 45 minutes.
Transfer soup to blender or food processor (working in batches if necessary) and puree. Return soup to pot and bring to a boil. Add rice at this point; cook until rice is tender. Adjust seasoning and serve, garnished with a few Parmesan shavings if desired.