Preheat your oven to 325°F (165°C). Pat the chicken pieces completely dry with paper towels — this is essential for a good sear. Season all over with salt and pepper, then lightly dredge each piece in flour, shaking off the excess.

In a large Dutch oven over medium heat, cook the lardons until the fat is rendered and they are golden and crispy, about 6 to 8 minutes. Remove with a slotted spoon and set aside, leaving the fat in the pot.

Increase heat to medium-high. Working in batches to avoid crowding, sear the chicken pieces skin-side down for 4 to 5 minutes until deeply golden brown. Flip and sear the other side for 3 minutes. Remove and set aside. Do not skip this step — the fond that builds in the pot is pure flavor.

Pour off all but 1 tablespoon of fat from the pot. Add the chopped onion, carrots, and garlic. Cook over medium heat, stirring occasionally, until softened, about 5 minutes.

Stir in the tomato paste and cook for 1 to 2 minutes until it darkens slightly and begins to stick to the bottom of the pot — this caramelization adds enormous depth.

Pour in the entire bottle of red wine, scraping up all the browned bits from the bottom of the pot with a wooden spoon. Add the chicken stock and nestle in the bouquet garni.

Return the seared chicken pieces and the cooked lardons to the pot. The liquid should come about two-thirds of the way up the chicken. Bring to a gentle simmer on the stovetop, then cover and transfer to the preheated oven.

Braise in the oven for 1 hour to 1 hour 15 minutes, until the chicken is completely fall-off-the-bone tender and the sauce has reduced and deepened in color.

While the chicken braises, melt 1 tablespoon butter in a skillet over medium-high heat. Sauté the mushrooms and pearl onions with a pinch of salt until golden brown, about 8 minutes. Set aside.

Remove the pot from the oven. Discard the bouquet garni. Transfer the chicken to a plate. If the sauce is thin, bring it to a boil on the stovetop and reduce for 5 to 10 minutes until it coats a spoon. Stir in the sautéed mushrooms and pearl onions.

Return the chicken to the pot. Just before serving, remove from heat and swirl in 2 tablespoons of cold butter until the sauce is glossy and silky. Taste and adjust seasoning. Serve immediately over mashed potatoes, egg noodles, or crusty bread, garnished with fresh thyme or parsley.