To make the bouquet garni, remove and reserve 8 leek leaves; remove white portion of leek leaves (reserve remaining leaves for another use). Flatten leek leaves. Place 3 thyme sprigs, 3 parsley sprigs, and 1 bay leaf lengthwise in each of 4 leek leaves. Top each filled leaf with one of the remaining leek leaves. Tie with string at 2-inch intervals.
Rinse chicken with cold water; pat dry. Trim excess fat. Remove and reserve giblets; discard neck. Remove skin; cut chicken into quarters. Mince giblets; set aside. Sprinkle chicken pieces with 1/2 teaspoon salt and 1/2 teaspoon pepper. Heat 1 tablespoon butter in a large Dutch oven over medium heat. Add chicken to pan; cook 10 minutes, browning on all sides. Remove from pan. Add bacon; cook until crisp. Return chicken to pan. Add bouquet garni, giblets, Calvados, 2cups broth, wine, and garlic; bring to a boil. Cover, reduce heat, and simmer 1 1/2 hours.
Remove chicken from wine mixture; cover and refrigerate. Cover and chill wine mixture 8 to 24 hours. Discard bouquet garni. Skim solidified fat from surface; discard.
Combine mushrooms and 2 cups broth in a large nonstick skillet; bring to a boil. Partially cover, reduce heat, and simmer for 30 minutes. Uncover and cook 10 minutes or until liquid almost evaporates. Sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper. Set aside.
Bring wine mixture to a boil. Reduce heat, and simmer for 20 minutes. Combine 2 tablespoons butter and flour in a small bowl; work into a paste with fingers or a fork. Add 1/4 cup wine mixture, stirring with a whisk until well-blended. Add butter mixture to wine mixture; bring to a boil. Reduce heat, and simmer 10 minutes. Return chicken and mushrooms to pan. Bring to a boil; reduce heat, and simmer 10 minutes or until thoroughly heated.
Wine Note: The quintessential French comfort food, Coq au Vin is traditionally served with a red Burgundy. An exemplary choice would be a sublime, earthy wine like Domaine de l'Arlot Nuits-St.- Georges Clos des Fôrets Premier Cur ($50). But a more hearty Rhône wine such as Domaine Santa Duc Côtes-du-rhône ($12.99) would be nearly as good, and its price is a little more in keeping with the accessibility of the dish.