Using a sharp knife, remove the tenderloin from the underside of the duck breast and reserve for another use. Trim any ragged bits or gristle from the underside of the duck, and then turn the breast over and trim any excess fat from the edges. Pat the duck completely dry with paper towels.
Place the duck, skin side up, on a cutting board. Score the skin with the tip of the knife by making shallow diagonal cuts, 1/2 inch apart, in one direction and then repeating in the other direction, creating a diamond pattern. Season both sides of the duck (that is, the skin side and the meat side) with the salt, then massage with the garlic paste (again on both sides), and then press the crushed peppercorns evenly onto the surface (again on both sides). Put the duck on a platter and set aside for at least 1 hour at room temperature. (You can instead cover and refrigerate the duck overnight; bring to room temperature before cooking.)
Heat a cast-iron skillet over medium-high heat until hot but not smoking. Carefully add the duck breast, skin side down, and let it sizzle for several minutes. Using tongs, check to see that the skin is not browning too quickly and that the garlic is not burning, and if necessary, reduce the heat. Be careful; the duck breast will render a fair amount of hot fat. Cook until the duck skin is golden and crisp, 6 or 7 minutes. Turn the duck breast over and cook for 2 minutes more. Transfer the duck to a carving board and let rest for at least 10 minutes. Reserve the rendered duck fat in the skillet, allowing it to cool to room temperature and then straining it into a jar and refrigerating it for future use.