Place the chicken and all of the marinade ingredients in a large bowl or ziplock. Make sure the wine covers the chicken pieces. Cover and refrigerate for 12 hours or overnight.
Remove the marinated chicken pieces and vegetables from the marinade. Pat them dry with paper towels until very dry. Keep them in separate plates/bowls.
Strain the wine marinade sauce with a fine mesh strainer. Skim off the scum on the surface of the broth, including black peppercorn, thyme, and bay leaf. In a sauce pan, simmer the sauce over medium heat. Cook until the liquid is reduced in half. Set aside.
In a large Dutch oven, add 1tbsp of oil. Cook lardons over medium-low heat until the fat has rendered, and lardons are golden and crisp about 4-8 minutes (depending on the thickness). Keep the grease in the pan. Transfer the lardons to a paper-towel-lined plate. Set aside.
In the same Dutch oven, heat the lardon fat or grease over medium heat until hot but not smoking. Working in batches, cook the chicken, skin side down until well browned for about 3-5 minutes each side. Don't overcrowd the pot! Transfer the chicken to a plate and set aside.
Add the marinated onions and carrots. Cook and stir often for 6 minutes, add minced garlic and cook for about 1-2 minutes. Add cognac/brandy, cook, stirring to scrape the brown bits from the bottom of the pan. Cook until the cognac has evaporated and reduced at least in half.
Add the reduced wine marinade sauce, browned chicken, chicken broth, half of the crispy lardons, 7 fresh thyme sprigs, 1 bay leaf into the Dutch oven, and bring to a simmer. Turn off the heat.
Preheat the oven to 250°F. Transfer the pot to the oven, covered and cook for 30-40 minutes or until the chicken is fully cooked and no longer pink.
While you're waiting, heat oil and butter in a large skillet over medium-high heat. Add pearl onions, a pinch of salt, and sugar. Lower the heat to low, cover the pan, and cook for 10-15 minutes or until caramelized, shaking the pan occasionally. Set aside.
In the same skillet, cook mushrooms for 5 minutes. Add the remaining lardons, stir for 1-2 minutes. Set aside.
Remove the pot from the oven. Transfer the cooked chicken and vegetables to a big plate. Strain the broth with a fine-mesh strainer. Discard all the garnish and to skim off the scum on the surface of the broth. Put the strained broth back into the Dutch oven, bring it to a simmer over medium heat. Add salt/pepper if needed. Stir in the beurre manie ( 2½ tablespoons butter + 2½ tablespoons flour), continue cooking and stirring for about 7 minutes or longer to reduce the liquid.
Add the chicken and vegetables back into the pot, simmer, uncovered for about 10 minutes. Add mushrooms, pearl onions, and crispy lardons. Bring to a boil and as soon as it boils, turn off the heat. Serve and enjoy with toasted french baguette slices.