Place the turkey carcass in a large stockpot and cover it with about 12 cups of water. Bring the water to a boil over medium-high heat.
Once boiling, reduce the heat to low and skim off any foam that rises to the surface.
Add the chopped onions, carrots, celery, minced garlic, bay leaves, thyme, and rosemary to the pot.
Season with salt and pepper to taste. Stir to combine.
Cover the pot and let it simmer on low heat for about 2 hours, allowing the flavors to meld and the broth to become rich.
After 2 hours, remove the carcass from the pot and let it cool slightly. Strain the broth through a colander into another pot to remove the vegetables and any small bones, discarding them.
Once the carcass is cool enough to handle, pick off any remaining turkey meat and return it to the broth. If using, add shredded turkey meat and frozen peas now.
Let the soup simmer for an additional 10-15 minutes until heated through. Adjust the seasoning if necessary.
Serve hot, garnished with fresh parsley if desired.