Prep the chicken: Pat the chicken dry and season generously with salt and pepper. This helps the skin crisp and builds flavor.
Crisp the bacon: In a heavy Dutch oven over medium heat, cook the diced bacon until browned and crisp. Transfer to a plate, leaving the fat in the pot.
Brown the chicken: Raise heat to medium-high.
Add the chicken skin-side down and brown well on both sides, about 4–5 minutes per side. Work in batches if needed. Transfer to the plate with the bacon.
Sauté the aromatics: If the pot looks dry, add a splash of olive oil.
Add pearl onions (or chopped onion) and cook until lightly browned, 3–4 minutes. Stir in garlic for 30 seconds, just until fragrant.
Deglaze and reduce: Pour in the brandy, if using, and let it bubble for 30 seconds, scraping up browned bits. Add the red wine and bring to a lively simmer.
Reduce by about one-third, 6–8 minutes. Stir in tomato paste and chicken stock.
Build the braise: Return bacon and chicken (plus any juices) to the pot. Add bay leaves and thyme.
The liquid should come about halfway up the chicken; add a bit more stock if needed. Bring to a gentle simmer.
Braise until tender: Cover and simmer on low for 35–45 minutes, or until the chicken is very tender and nearly pulling from the bone. You can also bake covered at 325°F (165°C) for the same time.
Cook the mushrooms: While the chicken braises, heat 1 tablespoon olive oil and 1 tablespoon butter in a skillet over medium-high.
Sear mushrooms with a pinch of salt until browned and tender, 5–7 minutes. Set aside.
Thicken the sauce: In a small bowl, mash the remaining 1 tablespoon butter with the flour to form a paste. When the chicken is done, transfer the pieces to a warm plate and tent with foil.
Skim excess fat from the pot. Whisk in the butter-flour paste a bit at a time and simmer until the sauce lightly coats a spoon, 3–5 minutes.
Finish: Return chicken, mushrooms, and any accumulated juices to the pot. Simmer 2–3 minutes to meld.
Taste and adjust with salt and pepper. Remove bay leaves and thyme stems. Garnish with parsley.
Serve: Spoon over mashed potatoes, buttered noodles, or creamy polenta.
A simple green salad on the side balances the richness.