Fill a pot or heat safe container with water, place your immersion circulator, and preheat the water to your desired temperature. I strongly recommend 180°.
Prepare the corned beef by removing it from its packaging.
Rinse 2-3 times in cold water, then pat dry with paper towels.
Score the fat cap. Use a sharp knife to make long, shallow cuts across the fat on top of the meat. Make the cuts about 2 inches apart on the diagonal in one direction and then again perpendicular to it. It should look like a sideways checker board.
Rub the meat with coarse mustard, caraway seeds, and black pepper.
Place the seasoned brisket into a vacuum bag or Ziploc bag along with sliced yellow onions and use the vacuum sealer to remove air and seal. See below for Displacement Method instructions.
Place in the preheated water bath for a minimum of 10 hours and a maximum of 12 hours. Check water levels at regular intervals to make sure vacuum bag is fully submerged.
Remove cooked beef from the water bath. Take it out of the sous vide bag and let excess water drip off onto a cutting board while the meat rests for 10 minutes.
Heat a skillet on medium-high heat. Once the pan is very hot, add cooking oil.
Place the brisket fat side down into the hot oil and let brown for 4-6 minutes until a nice crust has formed. Repeat on the other side.
Slice the corned beef brisket into thin pieces, cutting against the grain.
Serve with your favorite Irish side dishes.