In a large, heavy pan, heat 2 tablespoons of oil under medium high heat. Pat the brisket dry with paper towels on both sides. Sprinkle it with salt and pepper. Place the brisket in the pan and sear it on each side 3-4 minutes, until well browned. If there is slanted or raised portion on any part of the brisket that is not seared when both sides are done, press that part of the meat onto the pan long enough to sear it as well. Once the brisket is fully seared, remove it to the slow cooker, fat side up.

Add another tablespoon of oil to the pan. Slow cook the onions for 20 minutes, stirring frequently. They should look caramelized when done, although not as richly so as longer cooked caramelized onions. Remove the onions to the slow cooker, on top of the brisket. Add half (2 tablespoons) of the apple cider vinegar to the pan and scrape up any remaining bits of onion. Pour whatever remains over the brisket and onions and return the pan to the stove.

Add the final tablespoon of oil to the pan and heat it. Add the carrot and celery chunks, cooking them on medium-high heat for a few minutes until they begin to brown. Add the garlic and cook for an additional 30-60 seconds. Pour the vegetables into the slow cooker over the brisket and onions.

Mix the diced tomatoes, tomato paste, honey, and 2 remaining tablespoons of apple cider vinegar. Pour the mixture into the slow cooker over the brisket and vegetables. Turn the slow cooker onto low and cook for about 6 hours. Let the meat stand at least 30 minutes before serving (cutting it), although it is preferable to put the brisket and sauce into the refrigerator overnight and slice the meat the next day.