Place the rack in your electric roaster and pour in the beef broth. Unwrap the corned beef brisket (discard any spice packet that came with it) and place it fat-side up directly on the rack. Season the top generously with the freshly ground black pepper and scatter the smashed garlic cloves around it. Cover the roaster, set the temperature to 300°F, and let it begin cooking—this low, moist heat will slowly break down the tough brisket into tender, flavorful meat.
While the beef is cooking, prepare all your vegetables during the first hour. Cut the potatoes into 2-inch chunks, slice the cabbage into 3-inch thick wedges, quarter the onions, roughly chop the celery, and cut the carrots into 3-inch lengths. I like to keep everything in separate bowls by cooking time needed—this makes the next steps much smoother and prevents you from hunting for ingredients.
After the beef has cooked for 1 hour, carefully remove the roaster lid (watch out for the steam). Add all the potato chunks directly to the broth around the beef, nestling them down so they're partially submerged. This timing allows the potatoes to cook long enough to become tender but not so long that they fall apart. Cover the roaster again and continue cooking.
After the potatoes have cooked for about 45 minutes to 1 hour (about 1 hour 45 minutes to 2 hours total into cooking), add the cabbage, onions, celery, and carrots from Step 2 to the roaster, arranging them around the beef. Cover and continue cooking. I always check the internal temperature of the beef with a meat thermometer—you're aiming for 145°F for a tender result, which usually takes 1.5 to 2 more hours depending on the exact thickness of your brisket.
Once the beef reaches 145°F internal temperature, carefully remove it from the roaster and let it rest on a cutting board for 10 minutes before slicing—this keeps the meat juicy. The vegetables will continue to stay warm in the broth. Slice the beef against the grain into thick slices and arrange on a serving platter with all the vegetables. Pour some of the cooking broth over everything for serving.