Heat 2 tablespoons of butter in a large pot over medium heat. Add the chicken breasts, 1 teaspoon salt, and pepper.
Cook the chicken on each side for 3-4 minutes until browned, but not cooked through. Remove the chicken from the pot and set aside.
To the same pot, add the remaining 1 tablespoon of butter. Once melted, add the carrots, celery, and onion. Sprinkle with 1 teaspoon salt and the dried herbs. Cook until the carrots are tender, about 6-7 minutes.
Add the garlic, wild rice, and flour and cook for another minute. Pour in the wine and cook for 1-2 more minutes.
Gradually stir in the chicken broth.
Place the chicken back into the pot. Bring the mixture to a boil. Once boiling, turn down the heat and let it simmer, covered, for about 45 minutes until the wild rice is cooked and the chicken is fork tender.
Remove the chicken from the pot, shred it with 2 forks, and add the shredded chicken back into the pot.
Add the heavy cream and lemon zest and give the soup a good stir. Season the soup to taste with salt and pepper (and maybe a cornstarch slurry to thicken it up) and serve.