In a large soup pot or Dutch oven, sauté bacon in butter over medium heat until crisp and browned, about 5 minutes. Remove bacon with a slotted spoon and set aside.
Pat chicken dry with a paper towel and season with salt and pepper. Increase heat to medium-high; sear chicken in the butter/bacon fat until browned on all sides (about 5 minutes) – it does not need to be cooked through at this point. Remove from the pot and set aside.
Add carrots, celery, and onion to the drippings in the pot. Cook, stirring regularly, until the onion starts to soften, about 3 minutes. Add garlic and cook for 1 more minute. Stir in flour, bay leaf, Italian seasoning, basil, oregano, and thyme. Cook over medium heat for about 2 minutes, stirring constantly.
Add broth, potatoes, browned chicken (and any accumulated juices from the plate), and bacon to the pot. Bring to a boil; cover, reduce heat to low or medium-low, and simmer (covered) for about 15-20 minutes, or until the potatoes are tender. Discard bay leaf.
Stir in the cream. Simmer, uncovered, for about 5 minutes (or until heated through). Remove from the heat. Taste and season with additional salt and pepper, if desired. Stir in the parsley and a squeeze of fresh lemon juice. Ladle into bowls and garnish with chopped fresh herbs.