Thoroughly season spatchcocked chicken with salt and pepper. Fold wingtips underneath the chicken.
*See note above about spatchcocking a chicken.
Place butter in 12 inch cast iron skillet set over low heat. Wait until the butter melts and begins to brown.
Add chicken, skin-side down, to the skillet. Ensure the chicken is fully spread out. Sandwich the chicken between the skillet on the bottom and another heavy piece of cookware on top. Fill top cookware with cans of food for extra weight. The top cookware and food cans will ensure that as much skin as possible makes contact with the surface of the bottom skillet, resulting in an extra crispy skin. Cook over low heat for 25 minutes.
Remove chicken from skillet. Remove all the fat from the skillet except for 2 tablespoons. Wash the bottom of the cookware used to weigh down the chicken as you will be using it later.
Add onion and celery to skillet. Season with salt and pepper. Sweat the onions and celery for 5 minutes.
Add the garlic, dried sage leaves, and flour to the skillet. Quickly and constantly stir until flour is browned, and garlic and sage are aromatic, about 1 minute.
Slowly whisk in the chicken stock and vermouth/wine into the skillet.
Return chicken to the skillet, skin-side up, weighed down with the other piece of heavy cookware and food cans; braise for 45 minutes in a simmering gravy.
Remove chicken from skillet and place onto cutting board. Let rest for 10 minutes.
Meanwhile, allow gravy to come to a boil. Whisk in the lemon juice and zest, season gravy with salt and pepper, and remove skillet from heat.
Carve up the chicken and place onto plate. Spoon the gravy over the chicken and optionally garnish with parsley. Serve with potatoes or rice.