Heat a pot big enough to hold everything (6 quart dutch oven works) over medium low heat. Add the oil and then the leeks, onions and carrots. Cook, stirring occasionally, until onion and leek are soft but not brown. You won't get the carrots soft at this stage - don't bother trying. This takes about 7-10 minutes.
If you don't want bits of thyme floating in the broth, place it in a bit of cheesecloth. Tie securely with food safe string. Add the garlic and the 2 tsp salt and cook another 2 minutes. Add the thyme with the garlic and salt if adding it loose. If you are wrapping it in cheese cloth add it with the broth.
Pour in the stock. Let simmer, covered for about an hour. Add the diced turkey and let simmer another 10 minutes.
Add the egg noodles and cook until the egg noodles are tender, another 10 minutes or so.
Dissolve the cornstarch by adding it to a cup of cool water and stirring thoroughly. You don't want to be chasing lumps of cornstarch so get this right.
Add the cornstarch slurry to the soup. Bring to a boil. The soup will thicken noticeably.
At this point the soup is under salted. Add salt gradually until you are happy with the salt balance. Soup takes a lot of salt.