Heat a large stockpot over medium heat. When hot, add the sliced bacon and cook until crisp. Remove from pot onto paper towels. Leave any fat in the pot.
Add the cubed potatoes, leek, celery and carrot. Saute for roughly 5-7 minutes.
Stir in the thyme and garlic. Then, add chicken broth. Bring to a boil. Once boiling, reduce the heat and simmer, half-covered for 15-20 minutes, or until potatoes feel soft when pierced with a fork.
Add the shredded chicken and cook for a few more minutes, until chicken is hot. Stir in the cream and heat for another minute.
Serve in bowls, topped with bacon and more thyme, dill, or parsley.