In a large Dutch oven or heavy pot, cook the chopped bacon over medium heat until crispy, about 5-7 minutes. Remove the bacon with a slotted spoon and set aside, leaving the rendered fat in the pot.

Season the chicken pieces generously with salt and pepper. Increase the heat to medium-high and sear the chicken in the bacon fat for 4-5 minutes per side until the skin is deep golden brown, then remove and set aside.

Add the sliced carrots and chopped onion to the pot, sautéing for about 5 minutes until the onions are softened and translucent. Stir in the minced garlic and tomato paste, cooking for another minute until fragrant.

Pour in the red wine and chicken broth, scraping the bottom of the pot with a wooden spoon to release any browned bits (fond). Add the fresh thyme sprigs and return the chicken (and any accumulated juices) and crispy bacon to the pot.

Bring the mixture to a boil, then reduce the heat to low, cover, and simmer gently for 30 minutes.

Stir in the mushrooms and pearl onions, cover again, and continue to simmer for another 15-20 minutes until the chicken is cooked through and tender.

In a small bowl, mash the softened butter and flour together to form a paste (beurre manié). Stir this paste into the simmering stew and cook for 2-3 minutes until the sauce has thickened slightly and becomes glossy.

Remove the thyme sprigs and discard them. Garnish with fresh chopped parsley and serve hot, ideally over creamy mashed potatoes or with crusty bread to soak up the sauce.