Salt and pepper the duck liberally on both sides.
Place each half, skin side down, in a large, heavy-bottomed (preferably cast-iron) pan. Wedge the thyme and garlic under the skin.
Cover the pan with its lid or with foil, and place it over low heat. Braise for one hour (duck should crackle and sizzle gently; skin should be golden and crisp; most fat should be rendered).
Turn duck. Cover pan. Braise for another hour, until duck bottom is well browned and meat is quite tender.
Remove duck to a cutting board; with a poultry shear, halve the halves.
Place two Tbsp of the reserved fat from the pan into a clean sauté pan, and heat the pan to medium high. Place duck pieces skin side down, and sauté for 3 to 5 minutes, just until skin turns crisp and dark. Transfer to a dish.Serves 2 to 3