Pour the chicken broth into a large, heavy pot.
Rinse the chicken breast halves with cold water, and place in the pot with the chicken broth.
Bring the broth to a simmer, and cook the chicken for 15-20 minutes at low heat.
As the chicken is cooking, periodically skim the foam from the broth and discard.
Move the chicken to a dish to cool.
Pour the chicken broth into a bowl through a fine-mesh strainer, and set aside.
Wipe out the pot with paper towels.
Using the same pot, melt butter over medium-high heat.
Saute leeks and celery until soft, but not browned, for around 10 minutes.
Add mushrooms and saute for 2 or 3 minutes, then add the apple cubes and cook for another few minutes until the mushrooms and apples are soft.
Return the strained chicken broth to the pot with the vegetables; stir in apple cider vinegar, dried thyme, and cream.
Simmer for 20-30 minutes, partially covered.
In the meantime, cut the chicken into smaller pieces, then shred each piece by hand.
Cover the shredded chicken so it doesn’t dry out, and set aside.
After the broth and vegetables have simmered for 20-30 minutes, use an immersible hand-blender to puree the vegetables to a finer consistency.
Add the shredded chicken to the soup.
Season with salt and pepper, to taste.
Heat on low for at least 10 minutes.
Serve hot, and enjoy!
