Fill a medium pot with water and bring to a boil for the pasta.
While the pasta water is coming to a boil, heat the olive oil over medium heat in a large stockpot. Add the onion, carrot, and celery. Stir to coat and cook for 5-7 minutes or until the onion is translucent and the carrot has started to soften. Season with some sea salt and black pepper. Add the chicken stock, bring to a boil, and then reduce to a simmer. Add in the shredded cooked chicken and continue simmering while you get the pasta ready.
Once the pasta water is boiling, season generously with sea salt, and cook pasta until al dente. Drain the pasta and add it to the soup pot. Taste. Season as necessary with sea salt and black pepper. If the carrots or veggies are still not fully tender, continue simmering until they are ready to go. Ladle the soup into individual bowls and serve with a slice of crusty bread.