Pat the chicken pieces completely dry with paper towels and season generously on all sides with salt and pepper. Lightly dredge each piece in flour, shaking off any excess.

In a large Dutch oven or heavy-bottomed pot, heat the olive oil over medium-high heat. Working in batches to avoid crowding, sear the chicken pieces skin-side down for 4-5 minutes until deeply golden and crispy. Flip and sear the other side for 2-3 minutes. Transfer to a plate and set aside.

In the same Dutch oven, add the bacon pieces and cook over medium heat, stirring occasionally, until the fat has rendered and the bacon is golden and crispy, about 5-6 minutes. Remove the bacon with a slotted spoon and set aside, leaving the rendered fat in the pot.

Add the chopped onion and carrots to the pot and cook in the bacon fat over medium heat, stirring occasionally, until softened and beginning to caramelize, about 5 minutes. Add the smashed garlic and cook for another 1 minute until fragrant. Stir in the tomato paste and cook for 2 minutes, stirring frequently, until it darkens slightly.

Pour in the entire bottle of red wine and the chicken stock. Using a wooden spoon, scrape up all the browned bits from the bottom of the pot — this is pure flavor. Add the bay leaves and thyme sprigs. Return the seared chicken pieces and the cooked bacon to the pot, nestling the chicken into the liquid skin-side up. The liquid should come about halfway up the chicken.

Bring the liquid to a boil over high heat, then immediately reduce the heat to low, cover the pot, and simmer gently for 45-50 minutes, until the chicken is fully cooked through and very tender. For extra-tender results, you can place the covered Dutch oven in a 325°F (165°C) oven instead and braise for 1 hour.

While the chicken braises, melt 1 tablespoon of butter in a large skillet over medium-high heat. Add the pearl onions and cook, stirring occasionally, until golden and lightly caramelized, about 6-8 minutes. Transfer to a plate.

In the same skillet, melt the remaining 1 tablespoon of butter. Add the mushrooms in a single layer and cook without stirring for 3-4 minutes until they are deeply browned on one side. Stir and continue cooking for 2-3 more minutes. Season with salt and pepper and set aside.

Once the chicken is tender, carefully remove the chicken pieces from the pot and set aside. Discard the bay leaves and thyme sprigs. If the braising liquid looks thin, bring it to a boil over medium-high heat and reduce for 10-15 minutes, stirring occasionally, until it coats the back of a spoon with a glossy consistency.

Return the chicken, pearl onions, and mushrooms to the pot. Stir gently to combine and heat everything through for 3-4 minutes over medium-low heat. Taste the sauce and adjust seasoning with salt and pepper as needed.

Serve directly from the pot, garnished generously with fresh chopped parsley. Coq au Vin is traditionally served with buttered egg noodles, creamy mashed potatoes, or crusty bread for soaking up that extraordinary sauce.