Cut several very shallow crosswise slashes across the skin of each duck breast about 1/2 inch apart. (The cuts should only barely cut into the skin and fat; don't cut into the meat.) Season skin sides with salt, then generously season meat sides with salt, pepper, and thyme. Place into a heavy-duty resealable plastic bag, squeeze out all the air, and seal. Refrigerate for 1 hour.

Fill a large Dutch oven about 2/3 full with water and place over medium heat; heat to 135 degrees F (57 degrees C). Attach a candy thermometer to the side of the Dutch oven in order to monitor and maintain the water temperature. Place a silicone hot pad into the bottom of the pot to keep the plastic bag from contacting the bottom of the pan.

Place the sealed plastic bag into the Dutch oven. Cook, moving the bag around occasionally and adjusting the heat as necessary to maintain the temperature at 135 degrees F (57 degrees C), for 1 hour.

Remove duck breasts from the plastic bag and pat dry. Generously season skin sides with salt.

Heat oil in a skillet over high heat. Place duck breasts, skin-side down, in the hot skillet until fat renders and skin is golden brown, 5 minutes. Turn breasts over and cook until lightly browned and meat still pink in the center, 1 minute. Let rest for 2 minutes before slicing.