In a pot, combine carrots, celery, sweet potato, garlic, onion, and cover them with 8 cups of water. Add 2 teaspoons of salt and stir.
Bring to a boil over high heat, then reduce to low, cover, and simmer for 30-40 minutes until vegetables are tender.
Remove from heat and set aside 6 cups of vegetable water.
Strain the remaining water from the vegetables. Return vegetables to the pot and add 2 cups of reserved water.
Use an immersion blender to puree vegetables until smooth.
Add remaining water, salt, tomato paste, and ketchup to the pot. Bring to a boil.
Stir in ring pasta and simmer until cooked.
Remove from heat, season with salt, add optional parmesan and pepper, and serve.