Method
Prepare and brown the chicken
Pat the thighs completely dry and season both sides with salt and pepper. Place each thigh skin-side down on a cutting board and, working from the exposed flesh side, make a shallow cut about ½ inch deep along each side of the bone without cutting through the skin. This opens the thickest part of the thigh and helps the meat around the bone cook more evenly.
Arrange the thighs skin-side down in a cold, dry skillet. Unless the chicken has very little visible fat, there is no need to add oil. Turn the heat to medium-high and, as soon as the chicken begins to sizzle, reduce the heat to medium.
Let the thighs cook slowly for 12–16 minutes. Move them slightly after the first few minutes to make sure they haven’t stuck, but otherwise leave them alone long enough for the skin to brown and the fat to render. If the skin begins to darken too quickly, lower the heat.
Turn the thighs and cook the flesh side for about 2 minutes, then transfer them to a plate. They will not yet be fully cooked.
Brown the mushrooms and build the base
Pour off all but about 2 tablespoons of fat from the skillet. Add the mushrooms, spread them into an even layer and cook for 5–7 minutes, stirring only occasionally, until they release their moisture and begin to brown.
Once the mushrooms have taken on some color, add the shallots and cook for 2–3 minutes. Stir in the garlic and tomato paste and continue cooking for another minute, until the tomato paste darkens slightly and begins to stick to the bottom of the pan.
Add the cognac
Remove the skillet from the heat before adding the cognac. For the simple version, return the pan to low heat and let the cognac simmer for about a minute.
To flame it, keep the skillet off the burner and carefully ignite the cognac with a long lighter or butane torch. Keep your face, hair and sleeves well back and let the flame die out on its own. Never pour cognac directly from the bottle into a hot skillet.
Make the sauce and finish the chicken
Pour in the wine and use a wooden spoon to scrape up the browned bits from the bottom of the skillet. Let it simmer for 2–3 minutes, until it has reduced by about half.
Add the chicken stock, tomatoes, thyme and bay leaf, stir everything together and bring the sauce to a gentle simmer. Taste and add more salt if needed.