At least two days before serving, lay the duck legs skin side down on a platter and sprinkle with 1 tablespoon of the kosher salt and the ground pepper. Place the garlic cloves, bay leaves, and sprigs of thyme on two of the legs. Lay the remaining two legs skin side up on top. Put the reserved fat from the ducks in the bottom of a nonreactive container and top with the sandwiched duck pieces. Sprinkle with the remaining 1/8 teaspoon kosher salt. Cover tightly with plastic wrap. Refrigerate to cure for 12 hours.
Preheat the oven to 200°F.
Remove the duck from the container. Remove the garlic, bay leaves, thyme, and duck fat and reserve. Rinse the duck under cold running water, rubbing off some of the salt and pepper. Pat the duck dry with paper towels.
Put the reserved garlic, bay leaves, thyme, and duck fat in an enameled cast-iron pot or deep glass baking dish, and sprinkle evenly with the peppercorns and the 1/2 teaspoon salt. Lay the duck pieces skin side down on top and add enough olive oil to cover.
Cover and bake until the meat pulls away from the bone, 12 to 14 hours.
Remove the duck from the fat. Strain the fat into a bowl and reserve. Remove the meat from the bones and place it in a 1-quart stoneware or glass container; discard the skin and bones. Add enough of the strained fat to cover the meat by 1/4 inch. Cover and store in the refrigerator for up to 1 month. If you wish, pour the remaining fat into an airtight container and refrigerate to use as cooking fat.
Yield: 2 cups