Heat 2 tbsp butter in a large Dutch oven and add chopped bacon, frying until browned but not crisp.
Remove bacon to a side dish.
Dry chicken with paper towel and then sprinkle with salt and pepper.
Brown chicken in the bacon grease. You may have to do this a few pieces at a time.
Return bacon to the pot, cover and cook on medium-low for about ten minutes.
Turn off the heat and add cognac.
Avert your face and ignite the cognac with a lighted match then shake the pot gently for a few minutes until the flames completely subside.
Pour wine into the pot and add just enough chicken stock to cover the chicken.
Stir in the tomato paste, garlic and herbs.
Bring to a simmer.
Cover and simmer slowly for 25 to 30 minutes, or until the chicken is tender and juices run clear.
Remove the chicken to a casserole dish. (The chicken will have absorbed the red wine and be a weird purplish color but the sauce is going to cover it, so it will be fine.)
Place a large skillet over high heat and melt the butter and oil. When the butter is hot, add the mushrooms.
Stir gently every few minutes until lightly browned and tender, probably about ten minutes.
Remove the mushrooms to a bowl so you can use the same skillet for the onions.
Onions: melt the butter and oil in skillet until hot.
Add the onions and sauté over moderate heat for about ten minutes, stirring gently so the skins do not break. Brown as evenly as possible and then add the liquid, salt and pepper and thyme.
Cover and simmer slowly for about thirty minutes or until the onions are tender but retain their shape.
Simmer the chicken cooking liquid for a minute or two, skimming off the fat. Then raise the heat and boil rapidly, reducing the liquid to about 2 ¼ cups. Taste and add salt and pepper if needed. Turn off the heat and discard the bay leaf.
Blend the remaining 2 tbsp softened butter and 3 tbsp flour together into a smooth paste, then whisk into the sauce with a wire whisk.
Bring the sauce back to a simmer, stirring, and simmer for a minute or two. The sauce will thicken and should coat the back of a spoon.
Arrange the chicken in the casserole dish with the onions and mushrooms around it.
Pour the sauce over the chicken and serve.
Using too small a Dutch oven when searing poultry creates steam instead of the deep caramelization required for a rich braising base. When adapting classic French braises, maintaining the proper ratio of braising liquid to surface area ensures the sauce reduces correctly without overcrowding the pan. Accommodating smaller cooking spaces requires careful equipment selection and strategic timing adjustments.
Select a heavy-bottomed five-quart Dutch oven to ensure the chicken pieces fit in a single layer during the initial searing phase without trapping excess moisture.
When scaling down the volume of red wine and stock by half, monitor the reduction stage closely because smaller liquid volumes concentrate salt and acidity much faster than full batches.
Fresh pearl onions require peeling and precise browning to hold their shape, whereas frozen alternatives eliminate prep time while still caramelizing reliably when sautéed in a mix of butter and oil.
Whisking softened butter and flour together into a smooth paste before adding it to the simmering liquid prevents lumps from forming in the finished sauce.
Properly browned bacon fat provides the foundational flavor for searing the meat, so avoid wiping the Dutch oven clean between steps. Taking time to carefully ignite and burn off the cognac ensures all harsh alcohol notes dissipate before the wine is introduced.