In the bottom of a large Dutch oven, fry bacon pieces until crisp. Drain and reserve bacon. You should have 1 - 2 tablespoons bacon grease in the bottom of the pan. If not, add a little butter or neutral vegetable oil.
Depending on how much fat you like, you can remove the skin from the chicken pieces. Sear chicken pieces on all sides until golden brown. Reserve.
Again, add butter or oil so you have 1 - 2 tablespoons fat in the pan. Sauté the peeled pearl onions with a little salt and pepper until golden brown. Reserve. Add more oil or butter to the pan, if necessary, and sauté the mushroom pieces with a pinch of salt and pepper until golden brown. Reserve.
Add the carrot, celery, onion, and a pinch of salt and pepper and cook over medium heat until the vegetables are beginning to soften and turn golden.
Add the flour, and whisk and cook over medium heat for 1-2 minutes. Add the tomato paste and cook another minute or two. Deglaze the hot pan with a cup or so of wine.
Put the chicken back into the pan. Add the rest of the wine. Cover the pot and refrigerate overnight.
The next day, preheat the oven to 300°F, and add enough chicken stock to the pot to almost cover the chicken.
Tie the bay leaves, thyme, parsley, garlic cloves and peppercorns together in a square of cheesecloth and add to the pot. Submerge the bouquet garni in the cooking liquid.
Cover the pot tightly and let braise in the oven until the chicken is very tender, about 3 hours.
At the end of the cooking time, remove the chicken and the bouquet garni from the pot. Reserve the chicken and keep warm. Throw the bouquet garni away. Do not get the two confused and throw away the chicken.
With an immersion blender, blend the sauce until smooth, and then reduce on the stove top by about ¼ or until a nice saucy consistency.
Taste the sauce and add more salt and/or pepper, if needed.
Add back the reserved onions and mushrooms and heat through. Add the chicken back to the pan and stir everything together.
Spread the bacon pieces on a baking sheet and heat them up in the oven.
Garnish each serving with some of the hot, crispy bacon pieces.