Brown the Chicken:

Season the chicken pieces with salt and pepper. In a large Dutch oven or heavy pot, render the bacon until crispy. Remove and set aside.
In the same pot, brown the chicken pieces on all sides in the bacon fat. Remove and set aside.

Sauté Vegetables:

In the same pot, sauté pearl onions, carrots, and mushrooms until they start to color. Add garlic and cook for another minute.

Deglaze and Simmer:

Pour in the red wine and chicken stock, scraping the bottom of the pan to loosen any browned bits.
Stir in the tomato paste and add the bouquet garni. Return the chicken and bacon to the pot, ensuring the chicken is submerged. Bring to a simmer, cover, and cook on low heat for about 1.5 to 2 hours, or until the chicken is tender.

Thicken the Sauce:

Near the end of cooking, in a separate pan, melt the butter and stir in the flour to make a roux. Cook for a couple of minutes, then ladle in some stew liquid to create a smooth paste. Incorporate the paste back into the stew to thicken the sauce. Adjust the seasoning with salt and pepper.

Serve:

Discard the bouquet garni. Garnish the stew with chopped parsley and serve with mashed potatoes, rice, or crusty bread.