Add the carrots, celery, sweet potato, garlic, and onion into a pot. Cover the vegetables with 8 cups of water. Add 2 teaspoons of salt and stir.
Bring the pot to a rolling boil over high heat. Turn the heat to low and cover. Simmer for 30-40 minutes or until the vegetables almost fall apart at fork tender.
Remove the pot from the heat. Remove 6 cups of the vegetable water and set it aside.
Strain the rest of the water from the vegetables. Transfer the vegetables back into the pot and add 2 cups of the reserved water back into the pot.
Use an immersion blender to blend the vegetables and water into a thick puree until completely smooth.*
Add the remaining water, remaining salt, tomato paste, and ketchup to the pot and bring to a boil over medium/high heat.
Add the ring pasta to the pot and stir to combine. Turn the heat to medium/low and stir the pasta periodically to make sure the pasta isn’t sticking to the bottom of the pot.
Let the pasta simmer in the tomato sauce until cooked.
Remove from the heat. Salt to taste and add the optional parmesan and cracked pepper and stir. Serve immediately.