Place the chicken and 10 cups of water in a large pot. Partly cover and bring to a boil over high heat, keeping a close eye so that it doesn’t overflow and skimming off any foam that rises to the top.
Add the onion, olive oil, salt, garlic powder and pepper; stir and allow to come back up to a gentle boil. Cover completely, reduce heat to medium-low and simmer for 10 minutes. Add the carrots, celery, garlic and tomato paste, stirring to incorporate the tomato paste. I ncrease the heat to high and allow to come back up to a gentle boil. Cover, reduce the heat to medium-low and simmer for 30 minutes, stirring occasionally. Taste and season with more salt and pepper as desired.
Remove the cooked chicken and place in a large bowl. Add the pastina to the soup, stir and increase the heat to high and allow to come back up to a gentle boil. Cover, reduce the heat to medium-low and cook the pasta according to the package instructions for al dente, stirring occasionally.
While the pasta cooks, shred the chicken with a fork. Add the shredded chicken and parsley to the soup, stir, cover and simmer for 2 minutes. Serve topped with grated Parmesan.