Pat chicken dry with paper towel and sprinkle with salt and pepper. Set aside.
Cook bacon in a Dutch oven, or deep skillet with a lid, until crispy. With a slotted spoon, transfer bacon to a paper towel-lined plate; set aside.
Over medium-high heat, cook half of the chicken pieces, skin side down until browned, about 5 to 8 minutes. Flip chicken and brown the other side, about 5 minutes. Transfer to a plate and repeat with remaining chicken and transfer to plate.
Pour off all but one tablespoon of fat from pan, or add oil as necessary to achieve 1 tbsp. Reduce heat to medium. Add onions, carrots, and mushrooms and cook, occasionally stirring, until starting to lightly brown and onions are softened, about 10 minutes.
Stir in garlic and cook until it releases its fragrance, about 1 minute. Sprinkle flour over vegetables and cook, stirring, for 1 minute.
Stir in white wine, broth, bay leaves, and thyme scraping up any brown bits that may have accumulated.
Nestle in the chicken pieces with any juices and bring to a simmer. Cover and continue simmering gently for 1 hour or until the thickest part of the meat registers 165 degrees F.
Transfer chicken to a dish and tent with foil. Bring back to simmer and cook until sauce is thickened. Remove from heat and stir in half of the bacon, 2 tablespoon parsley, and heavy cream, if using. Taste and season with salt and pepper. To serve either pour sauce over the chicken or pour sauce into a serving dish and place chicken on top. Sprinkle with the remaining bacon and parsley.