Generously sprinkle the duck with kosher salt and freshly cracked black pepper. For optimal flavor, leave uncovered in the refrigerator overnight before moving on to the next step.
Enclose the duck in vacuum-sealed bags. Immerse the bags in a water bath set at 130°F (54°C) for a minimum of 45 minutes, and no more than 4 hours. Take the duck out of the bags and pat dry completely with paper towels.
Arrange the duck breasts with the skin side facing down in a sturdy 12-inch non-stick or cast iron skillet. Position the skillet over high heat and cook until you hear sizzling, approximately 2 minutes. Lower to medium heat and continue cooking, moving and pressing the breasts to ensure the skin makes good contact with the pan until the skin is golden brown and crispy, about 5 minutes. Turn the breasts over and cook the other side until it is lightly colored, around 30 seconds. Move them to a plate lined with paper towels and let them rest for 5 minutes.
Cut the breasts into 1/2-inch slices across the grain and serve.
Notes
Pat the duck breasts dry with paper towels before cooking for a crispy skin.
Cook the duck breasts skin-side down first to achieve a crispy texture.
Slice the duck breasts against the grain for more tender and easier-to-eat pieces.