Heat the olive oil in your stockpot over medium heat. Add the onion, carrots, and celery, and cook for about 5 minutes, stirring occasionally. You want them soft and fragrant, not browned, so keep the heat moderate the whole time.
Stir in the minced garlic, thyme, and rosemary, and cook for another 30 seconds until you can really smell them. This short step wakes up the spices before the liquid goes in, which makes a noticeable difference in the final flavor.
Add the turkey or chicken broth along with the bay leaf, then raise the heat and bring everything to a gentle boil. Once it's bubbling, reduce the heat back down to a simmer so the vegetables keep cooking gently.
Let the soup simmer uncovered for about 15 minutes, or until the carrots are fork-tender. This is when the broth really starts pulling flavor from the herbs and vegetables, so don't rush this part of the process.
Stir in your shredded leftover turkey and the egg noodles or pasta, if using. Continue simmering for another 8 to 10 minutes, or until the noodles are cooked through but not mushy.
Add the frozen peas and cook for 2 more minutes just to warm them through. Taste the soup, season with salt and pepper, remove the bay leaf, and sprinkle fresh parsley on top before ladling into bowls.