Remove giblets and neck from chicken and set aside. Rinse both chickens under cold water. Place one whole chicken, breast side down, on a cutting board. Using poultry scissors, cut along each side of the back bone, making sure to remove ribcage. Spread chicken open and cut through the center of the breast bone to separate chicken into two halves. Place each half skin side up; remove wings at the joint where they are attached to the breast. Separate leg and thigh from breast, cut to separate. Repeat process with second chicken. Transfer breasts and legs to refrigerator.
Place backs, wings, and necks (if included) in a large saucepan; add 8 cups water. Bring to a boil over high heat; immediately reduce heat to a low simmer. Simmer for 2 hours, skimming impurities from the top as stock cooks. Strain stock through a fine mesh sieve into a large container; discard solids. Stock can be made up to 1 day ahead and kept refrigerated until ready to use.
Remove chicken pieces from refrigerator and season with salt and pepper. Dust chicken lightly with flour. Heat canola oil in a large heavy-bottomed pot over medium heat. Working in batches, add chicken and cook, turning, until golden brown and crisp on all sides. Remove chicken from pot and set aside.
Drain all but 1 tablespoon oil from pot. Add bacon, if using, and cook until fat is rendered and bacon is crisp. Add celery, carrot, onion, garlic, and mushrooms; cook stirring, until lightly caramelized, 5 to 7 minutes.
Meanwhile, add wine to a medium saucepan. Bring to a boil over medium-high heat; let boil for 4 minutes.
Add 2 tablespoons flour and tomato paste to pot with vegetable mixture. Add brandy to deglaze and return chicken to pot along with heated wine, 2 cups of the chicken stock (reserve any remaining chicken stock for another use), thyme, parsley, bay leaf. Bring liquid to a boil and immediately reduce heat to low; simmer until chicken is tender and begins to fall of the bone, about 2 hours.
Carefully remove chicken from liquid and set aside; remove bacon and discard. Bring liquid to a boil; immediately reduce to a simmer. Let simmer until liquid is thickened and reduced by half. Return chicken to pot; season with salt and pepper. Serve with egg noodles.