Lay the leg portions on a platter, skin side down. Sprinkle with 1 tablespoon of the kosher salt and black pepper. Place the garlic cloves, bay leaves, and sprigs of thyme on each of 2 leg portions. Lay the remaining 2 leg portions, flesh to flesh, on top. Put the reserved fat from the chicken in the bottom of a glass or plastic container. Top with the sandwiched leg portions. Sprinkle with the remaining 1/8 teaspoon kosher salt. Cover and refrigerate for 12 hours.
Preheat the oven to 200 degrees F.
Remove the chicken from the refrigerator. Remove the garlic, bay leaves, thyme, and chicken fat and reserve. Rinse the chicken with cool water, rubbing off some of the salt and pepper. Pat dry with paper towels.
Put the reserved garlic, bay leaves, thyme, and chicken fat in the bottom of an enameled cast iron pot. Sprinkle evenly with the peppercorns and salt. Lay the chicken on top, skin side down. Add the olive oil. Cover and bake for 12 to 14 hours, or until the meat pulls away from the bone.
Remove the chicken from the fat. Strain the fat and reserve. Pick the meat from the bones and place it in a stoneware container. Cover the meat with some of the strained fat so that there is a 1/4-inch layer of fat on top. The chicken confit can be stored in the refrigerator for up to 1 month.
The excess oil can be stored in an airtight container in the refrigerator and used like butter for cooking. The tinge of chicken taste in the oil is wonderful and I use the oil to roast potatoes, cook green beans, and pan-fry veal.