Pat chicken pieces very dry with paper towels. Season generously all over with 1 teaspoon salt and 1/2 teaspoon black pepper.

In a large Dutch oven or heavy-bottomed pot, cook the bacon lardons over medium heat until crispy and browned. Remove the bacon with a slotted spoon and set aside, leaving the rendered fat in the pot.

Increase heat to medium-high. Add 1 tablespoon olive oil to the pot if needed. Sear the chicken pieces, skin-side down first, in batches if necessary, until deeply golden brown on all sides, about 5-7 minutes per side. Remove chicken from the pot and set aside.

Reduce heat to medium. Add the remaining 1 tablespoon olive oil to the pot. Add chopped onion and sliced carrots and cook, stirring occasionally, until softened, about 5-7 minutes. Add minced garlic and cook for another minute until fragrant.

Sprinkle the flour over the vegetables and stir constantly for 1-2 minutes to create a roux.

Carefully pour in the brandy. Stand back as it may flare up. Scrape up any browned bits from the bottom of the pot. Let it cook for 1 minute until mostly evaporated.

Stir in the red wine, chicken stock, and tomato paste. Add the bay leaves and fresh thyme bundle. If using, stir in the sugar. Bring the sauce to a simmer, scraping the bottom of the pot to loosen any remaining stuck-on bits.

Return the seared chicken pieces to the Dutch oven, nestling them into the sauce. The chicken should be mostly submerged.

Bring to a gentle simmer, then reduce heat to low, cover the pot, and cook for 75-90 minutes, or until the chicken is very tender and cooked through, easily falling off the bone.

While the chicken braises, heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add the quartered mushrooms and cook, without stirring too much initially, until deeply browned and tender, about 5-7 minutes. Remove and set aside.

In the same skillet, add the pearl onions (if fresh, you might need to blanch and peel them first; frozen just add directly). Cook until tender and lightly caramelized, about 5-8 minutes.

Once the chicken is tender, remove it from the pot and set aside. Skim any excess fat from the surface of the sauce. Remove and discard the bay leaves and thyme bundle.

If the sauce is too thin, increase the heat and gently simmer, uncovered, for 10-15 minutes, or until it reaches your desired consistency.

Return the chicken, cooked bacon, sautéed mushrooms, and pearl onions to the pot. Stir gently to combine and heat through for a few minutes.

Taste and adjust seasoning if necessary.

Ladle into bowls, garnished generously with fresh chopped parsley. Serve hot with mashed potatoes, crusty bread, or egg noodles.