Place the turkey legs and next 3 ingredients in a roasting pan and spray contents liberally with pan spray. Place in a preheated 400 degree oven and brown legs and vegetables evenly, turning once or twice while roasting.
Remove contents and transfer to a large stockpot. Add some water to the roasting pan to loosen any bits stuck to the pan. Pour liquid into stockpot. Fill pot with cold water, about an inch over contents of pot. Bring to a boil and then lower heat and simmer over low heat for 4 – 6 hours. Add water as needed to just cover contents of pot.
Place a colander (preferably lined with cheesecloth) over another stockpot. Pour contents of simmered legs, etc. through the colander into the new pot. Reserve contents of colander and allow to cool. You should have roughly 1 1/2 quarts of liquid. If more liquid is needed, add some water or, better yet, chicken broth.
Add diced tomatoes, onion, garlic and carrots to the pot and simmer over medium heat for 10 minutes. When turkey legs have cooled, remove meat and add to pot.
Add remaining vegetables and cook for 5 minutes. Add pasta and cornstarch mixture and cook for 5 minutes more.
Spoon soup into bowls and top with cheese.