Preheat oven to 375°F. Line a rimmed baking sheet with parchment paper and set aside.Place all meatball ingredients in a large mixing bowl. Using your clean hands, gently mix until well combined. Form small meatballs, using either a Tablespoon measure or a 1¼ inch mini scooper and arrange on baking sheet. Roast meatballs for 18-20 minutes until meatballs are well browned. Remove from oven and set aside. While meatballs are roasting, heat olive oil in a large stockpot or Dutch oven over medium heat. Add carrots, celery and onion and sauté over medium heat for 6-8 minutes. If veggies start to burn or brown too quickly, add ¼ cup water to pan and continue cooking until veggies have softened and become translucent.
Add tomato paste and stir well, until all the vegetables are coated in the tomato paste. Cook for an additional 4-5 minutes until everything is well browned. There is flavour in the brown, you are developing deep flavours here. Add Aleppo, oregano, thyme, bay leaves, salt, and pepper and stir well.
Add canned tomatoes and stock. Stir well, scraping up any bits stuck to the bottom of the pot. Add potatoes, squash, zucchini, and Parmesan rind. Increase heat to high and bring mixture to a boil. Once boiling, turn down to simmer, partially cover the pot and simmer soup for 15-20 minutes, until potatoes and squash are tender.
Remove lid, add beans and pasta and simmer, uncovered for an additional 15 minutes. Add kale and meatballs and simmer for another 5 minutes, until pasta is cooked. Remove bay leaves and Parmesan rind and discard.
Just before serving, stir in 1 Tablespoon vinegar.
Ladle soup into bowls and top with grated parmesan cheese.