Cut the chicken into eleven pieces (by cutting the whole breast into five pieces). Season it with salt and set aside.
In a roasting pan over medium heat, fry the bacon until crisp.
Raise the heat a little and add the chicken, along with the garlic, thyme, bay leaves, basil, peppercorns, carrot, celery, and mushrooms. Sear the chicken in the bacon fat until browned all over, turning it every two minutes or so. Cover the pot between turnings.
Pour off the excess fat from the pan. Add the brandy and (if your kitchen is safe for doing so) flame it if you like. Otherwise, let the brandy just simmer away to nearly nothing.
Add the wine, cover the pan, and put it in the oven at 425 degrees for about an hour and fifteen minutes. It will be ready when the chicken is falling away from the bone.
While the chicken is in the oven, make a medium-dark roux with the butter and flour. When it's almost the color of an old penny, remove it from the heat. Keep stirring until it cools enough that it's no longer cooking.
Remove the chicken and strain the solids out of the sauce. Whisk the roux into the sauce. You may not need all of it to give the sauce a pleasant consistency.
Remove the bay leaves and return the vegetables to the sauce. Add the pearl onions and cook over medium heat until the sauce bubbles a little.
Divide the chicken among four plates, and pour the sauce over it.