In a bowl, combine the salt and spices. Sprinkle the spice mixture over the chicken, emphasizing on the thighs and breast. Place in a baking dish. Cover with plastic wrap and refrigerate for 24 hours.
With the rack in the middle position, preheat the oven to 400 °F (200 °C).
In a bowl, combine the butter and mustard. Pat the chicken skin dry with paper towels. Coat the chicken with the butter mixture. Bake for 30 minutes. Reduce the oven temperature to 350 °F (180 °C). Bake for an additional 1 hour and 15 minutes or until a thermometer inserted into the thigh without touching the bone reads 180 °F (82 °C).
Meanwhile, in a saucepan, soften the shallot and garlic in the butter. Add the flour and cook, stirring constantly, until the mixture begins to brown, about 2 minutes. Deglaze with the liquor. Add the mustard and broth. Bring to a boil. Simmer for about 45 minutes or until the sauce has reduced by half.
Transfer the chicken to a platter and serve with the cognac sauce.
The chicken is baked at 400 °F (200 °C) for the first 30 minutes, both to brown the chicken and so that it allows you to simultaneously bake an Apple-Cheddar Tart on the lowest rack of the oven.