The day before: Peel, wash, and thinly slice the carrots into rounds. Slice the onions and remove the germ from the garlic cloves. Place half of these ingredients in a large dish, add the coq pieces, then top with the remaining vegetables.

Pour in the wine, a splash of cognac, bay leaf, thyme, parsley, salt, and pepper. Drizzle with a thin layer of oil and cover tightly. Marinate for at least 12 hours, turning the pieces occasionally.

The next day, drain and pat dry the coq pieces. Strain the marinade and bring it to a boil, skimming off any foam. Brown the coq pieces on all sides, starting with the skin side down, in a mixture of butter and oil. Remove and set aside.

Add the aromatic vegetables from the marinade to the pot and sauté. Return the coq pieces, degrease if needed, and flambé with cognac. Add the marinade and let it reduce. Pour in the chicken stock and season to taste.

Simmer for 1 1/2 to 2 1/2 hours, depending on the age of the coq. Cook slowly and steadily, adding more chicken stock if the sauce reduces too much.

Slowly cook the pearl onions in butter until glazed. Brown the bacon or pancetta, drain excess fat, and set aside. Clean and slice the mushrooms, then sauté them in the bacon fat. Chop the parsley.

Check that the coq is cooked through. Remove the pieces, skim the fat from the sauce, and check the thickness (reduce further if needed). Return the coq, bacon, mushrooms, and pearl onions to the pot. Simmer everything together for 20 minutes and serve hot.