Put the chicken pieces in a large bowl, and add the buttermilk, 1 teaspoon salt, 1/2 teaspoon black pepper, the thyme, and 4 of the garlic cloves. Marinate for at least 1 hour at room temperature or, refrigerated, overnight.
Preheat the oven to 350 degrees F, and set a baking sheet fitted with a rack on the middle shelf.
Meanwhile, prepare the chicken coating: Combine the 1 1/2 cups flour, the ground crackers, 1 3/4 teaspoons salt, 1 teaspoon pepper, and the paprika in a large bowl. One at a time, take the chicken pieces from the buttermilk and dunk them in the flour dredge, pressing hard to make the coating adhere to every spot. Set aside on a plate.
In a large, high-sided cast-iron pan, add lard or oil to a depth of 1 inch. Heat over medium-high heat until a droplet of water sprinkled on the surface sizzles loudly.
Give the chicken pieces a fresh roll in the flour mixture if they've absorbed it, and add as many pieces of the dark meat (thighs, wings, and drumsticks) as will fit comfortably in the pan. Fry, turning as needed, until all sides turn dark golden brown, 8 to 10 minutes. Transfer the cooked chicken to the baking sheet in the oven. Continue frying the rest, saving the white breast meat until last, and being careful not to burn the residue forming at the bottom the pan; that's your gravy base. When it is browned, add the chicken to the baking sheet. (Ideally the dark meat should bake in the oven for about 20 minutes and the light meat for about 10 minutes, until cooked through.)
Pour off most of the fat in the pan, leaving 2 tablespoons of oil and the brown sludge at the bottom of the pan. (But if any of it looks burnt, discard that as well, because that is the base of your gravy.) Let the pan cool down for a minute. Then add the remaining 3 garlic cloves and the sage, and fry for 1 minute. Add the remaining 5 teaspoons flour and cook, stirring, until the mixture is smooth and light brown, about 2 minutes. Add the stock and whisk until smooth. Cook the gravy over low heat until it thickens softly, about 5 minutes.
Season the gravy with salt and pepper to taste, remove the garlic and sage, and pour it into a spouted pitcher to pass behind the hot chicken and the mashed potatoes.
Adapted from "The New Midwestern Table" by Amy Thielen (c) Clarkson Potter, 2013. Provided courtesy of Amy Thielen. All rights reserved.