Rinse wild rice under cold water using a strainer. This removes dirt and makes it taste better and cleaner.
Melt butter in your big pot over medium heat. Wait until it gets foamy and smells really good all over.
Add onion, carrots, and celery to the pot. Cook for 6-7 minutes until soft. Stir them around so they don't stick.
Throw in the minced garlic and cook for 1 minute. Stir constantly so the garlic doesn't burn at all on the bottom.
Add wild rice, broth, and thyme to the pot. Turn the heat to high and bring it to a big rolling boil.
Turn the heat to low, put the lid on, and simmer 40-45 minutes. The rice should get tender and a bit chewy.
Stir in shredded turkey and simmer 10 more minutes. This heats the turkey all the way through nicely and evenly.
Add heavy cream, salt, and pepper. Stir gently and don't let it boil. Boiling will make the cream look weird and separated.
Take it off the heat and let it rest 5 minutes. This helps all those yummy flavors blend together really nicely.
Scoop into bowls, sprinkle fresh parsley on top, and serve hot. Grab some bread or salad to go with it!