To cook one duck, you need about 2 1/2 cup duck fat. A 4.5 lb. duck renders at least 1 cup of fat. Ask your butcher for extra duck fat, or you'll need another cooking fat to supplement. I'd use a mild lard; it's flavor isn't obtrusive. A 4.5 lb. Long Island duck typically yields about 8 oz confit meat (equal parts leg and breast meat).
PREPARE THE DUCK: Cut the legs and each breast half from the duck. Trim any excess skin and fat from the legs and save for rendering.
Gently but firmly pull the skin from the breast meat. Set the skin aside and put the breast and legs in a baking dish.
Sprinkle liberally with the salt. Nestly the bay leaves, thyme and garlic among the duck pieces. Cover with plastic and refrigerate for 24 hours.
RENDER THE FAT: Trim all the skin and fat from the carcass. Put the skin and fat, including the skin from the breasts and trimmings from the legs in a small heavy saucepan over low heat. Cook, partially covered, at a gentle simmer, stirring occasionally to prevent the skin from sticking.
After about 1 1/2 hours, the skin will be a deep golden in color and crisp, meaning it has rendered almost all of its fat. Take the pan off the heat and let it cool slightly.
Strain the fat into a container, seal it, and refrigerate until ready to use. The crisped skin may be eaten or discarded.
COOK THE DUCK: In a heavy, 1 1/2 qt saucepan, melt the rendered fat over low heat. Blot the duck pieces with paper towels to remove any excess salt and to dry them. Put the duck in the pan, along with garlic, thyme and bay laves. Arrange the pieces so that they're all submerged. If needed, add more lard.
Cook, uncovered, at a very gently simmer, between 185 degrees and 195 degrees, for 2 hours. Do not stir, and never let it boil. After 2 hours, the duck confit will be very tender and will come easily off the bone.
Lift the duck from the fat using tongs and either use imediately or cool and store, covered, in the refrigerateor for up to a week.