In a 2- to 3-quart pan over high heat, boil wine, uncovered, until reduced to 1 1/2 cups, 12 to 15 minutes.
Meanwhile, in a 12-inch frying pan or 6- to 8-quart pan (with sides at least 3 in. high) over medium-high heat, stir bacon often until browned and crisp, 8 to 10 minutes. With a slotted spoon, transfer to paper towels to drain. Discard all but 2 tablespoons fat in pan.
Rinse chicken and pat dry; trim off and discard any excess fat. Sprinkle pieces lightly all over with salt and pepper. Put 1/3 cup flour in a shallow bowl. Press pieces into flour, turning to coat all sides; shake off excess (discard any remaining flour). Add half the chicken to pan over medium-high heat and turn as needed until well browned on all sides, 4 to 6 minutes total. As chicken is browned, transfer to a large bowl and add remaining chicken to pan to brown.
Add 1 tablespoon garlic, carrots, onions, and mushrooms to pan. Stir often until lightly browned, 10 to 12 minutes. While vegetables brown, wrap parsley and thyme sprigs, bay leaves, and peppercorns in a double layer of cheesecloth, 10 inches square; tie closed with heavy cotton string. Add cognac to pan and stir to scrape browned bits free. Return all chicken except breast pieces, plus any accumulated juices, to pan and add reduced wine, bacon, herb bundle, and broth.
Bring mixture to a boil over high heat, then reduce heat, cover, and simmer for 20 minutes. Add breast pieces and simmer, turning pieces over in liquid occasionally, until meat is very tender when pierced, 25 to 30 minutes longer. With a slotted spoon, lift chicken and vegetables from pan, and divide equally among four wide, shallow bowls; keep warm in a 200° oven. Skim and discard fat from liquid. Boil over high heat, uncovered, until reduced to about 2 cups, 10 to 12 minutes. Pour equally over chicken and vegetables.
Sprinkle remaining 1/2 tablespoon garlic and the minced parsley evenly over portions of coq au vin, and set two toast triangles alongside.