1. Cut the duck breasts into halves and trim off any overhanging fat. Score the skin with a sharp knife in a diamond pattern. Pat dry and sprinkle with salt, pepper, cinnamon, and cayenne. Refrigerate, skin side up and uncovered, for several hours.
2. Before cooking, pat the skin dry again and place the breast halves skin down into a cold cast iron pan. Cook on low for about 8 minutes. The skin will slowly crisp and the fat will melt without burning the skin. It might take a few minutes more or less -- make sure to check the skin side occasionally. Look for a golden brown skin and an almost nonexistent layer of fat underneath.
3. Flip the breast and finish cooking on the other side. Do this for 3 minutes if you like it rare, or for longer, depending on your preference. Let the breasts sit for at least 5 minutes before cutting into them.
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