To start, you need to remove the meat from the carcass in one piece. Have at hand a large cutting board, a bowl, a damp kitchen towel and a very sharp knife. If you have a boning knife, all the better, but a sharp knife, with a very sharp tip, is most important.
Place a paper towel under the cutting board to keep it from sliding. Make sure all the good stuff from the carcass — the neck, gizzard, heart and liver — has been removed and reserved. Also remove the two big pieces of fat attached to either side of the large cavity. You’ll be rendering that fat later.
Rinse the goose well and pat it dry. Place a paper towel on top of the cutting board, under the goose, to keep the bird from sliding around. Then, place the goose on the board breast-side up, with its legs facing you.
Feel for the breastbone, running right down the center. Make one deep and daring slice through skin, fat and meat, right to the breastbone, from top to bottom. Press the knife tip against the bone, just to the right of the ridge of the breastbone. Divide the neck skin along the same line.
Work the tip of your knife against the breastbone and ribs, pulling the breast meat gently away from the bones as the knife releases the meat. Work one side and then the other. You can’t go terribly wrong here if you stay close to the rib bones with the tip of your knife, making short slices, not long strokes. Work slowly, deliberately and methodically with the knife, and use your other hand to pull the meat away. There is no need to rush. It’s akin to removing a coat, peeling each side back as you go. Stop when you run into the wings and thighs.
Lift the carcass and press down on the leg quarter, right at the knee. Bend back the thigh toward the cutting board, exposing the joint between the main carcass and the thigh bone. Wriggle the knife into that joint and separate the bones. Repeat on the other side. Using the same motion, disjoint the wings and then continue to remove the “coat,” using the knife to release the carcass when you reach the backbone.
Spread out the skin and meat, skin side down, and slice each breast half free of the skin, making it look very tidy. Make a similar cut around the meat of the thighs, forming the leg quarters.
Wrap the two breast halves and two leg quarters in plastic wrap and refrigerate until you’re ready to make the braise.
Render the fat
On the board before you will be a stripped carcass, a lot of skin and some pieces of meat — all useful, delicious and not to be wasted. A goose is an investment, and there is a world of flavor on that cutting board.
Gather any trimmed meat in a bowl. Cut around and release the wings and add them to the bowl. Sprinkle with a teaspoon of kosher or sea salt and one minced garlic clove and stir well. Cover and refrigerate for eight to 24 hours.