Heat a large skillet over high heat. Once hot, add the oil, carrot, onion and celery. Stir to blend and season with salt. Cook until the vegetables become tender and slightly caramelized, 10-12 minutes. Transfer the vegetables to a bowl and refrigerate to cool them down.
In another bowl, mix the ground brisket with the mayonnaise. Season with salt to taste. Mix in the vegetables. Form the meat into eight even patties that are about 3/4 inch thick.
Place the hamburgers on the hottest part of the grill and cook, undisturbed, for about 2 minutes. Turn them a quarter turn and cook for 2 more minutes. Use a metal spatula to flip them on their second side and cook for an additional 2 minutes for rare to medium rare. Toast the bun halves on the coolest part of the grill. Butter each one. In the last 2 minutes of cooking, add the cheese on top of each burger to allow it to melt as the burgers finish cooking. Place a hamburger on a "bottom" bun half and top with some red cabbage slaw (see recipe below). Top with a bun "top" and serve immediately.
Red Cabbage Slaw:
In a large bowl, combine the cabbage and minced Jalapeno with the dill pickle and dill pickle juice. Toss to blend. In a separate bowl, whisk together the sour cream and cider vinegar with the salt, sugar and black pepper. Pour the sour cream mixture over the cabbage and toss to blend. Refrigerate until ready to use.