Chop the onions and celery, then mince the garlic. Set aside.
Rinse the chicken pieces in cold water, then pat dry with paper towels. Set aside on two large plates.
Mix together the flour and seasonings in an 8x8-inch pan. Coat each piece in the flour mixture. Reserve ½ cup (60g) of the leftover flour for making the roux.
Melt the butter in two large skillets over medium high heat. Place 6 or 7 pieces of coated meat in each skillet, making sure they aren't touching.
Brown the pieces by cooking it for 5 minutes per side, until the skin is golden brown. After a couple of minutes of cooking, turn down the heat to medium low. Drain it on a paper towel-lined cookie sheet.
Pour the fat from the two skillets into a bowl, then add 2 tablespoons back into each skillet.
Divide the onion and celery between the two skillets, then turn to medium high heat. Sprinkle the vegetables with kosher salt and black pepper and saute for 5 minutes, stirring occasionally. Add the garlic and cook for 1 minute, stirring constantly.
Lower the heat to medium. Add 3 tablespoons of the reserved flour mixture to each skillet to create a roux. Whisk the flour with the fat and vegetables and cook for a minute. Slowly add 1 ½ cups (354 ml) of broth to each skillet, whisking constantly to prevent lumps. Cook the Southern gravy for two minutes, until thickened. (If you want more gravy, double it now.)
Add the browned chicken pieces back to the skillets and coat each piece with the gravy. Top with the fresh thyme and fresh sage. Cover the skillets with lids or aluminum foil to speed up the cooking time and to prevent the gravy from reducing.
Cook over medium low heat for 40 minutes, or until the meat is falling off the bone. Turn the chicken after 20 minutes of cooking. If necessary, add ½ cup stock to each skillet to create more gravy. The meat thermometer should read 165 F when inserted into the thickest part of the meat. If you prefer, you can place your covered cast iron skillet in a 350F oven for 35 to 40 minutes.
Garnish your Southern smothered chicken with fresh thyme leaves. Serve warm over rice, mashed potatoes, or with a crusty bread to sop up the gravy.