Place 2 cups of the bbq sauce in a large shallow baking dish, add the brisket and turn to coat. Cover and marinate in the refrigerator for 4 hours or overnight. Preheat oven to 325 degrees F. Heat the vegetable oil in a large Dutch oven over high heat until smoking. Remove the brisket from the dish, season with salt and pepper and sear well on both sides and remove to a plate. Add the carrots, onions, celery and garlic and cook until soft and golden brown. Return the brisket to the pan and cover with the chicken stock, water and the remaining 1 cup of bbq sauce. Bring to a simmer on top of the stove, cover and place in the oven. Cook for 2 1/2 to 3 hours or until tender. Remove from the cooking liquid, let rest for 15 minutes then slice thinly on the bias.
Red Cabbage Slaw:
Place cabbage in a large nonreactive bowl. Bring vinegar, honey and salt and pepper to a simmer in a medium saucepan. Pour the warm mixture over the cabbage and stir to combine. Cover with plastic wrap and let rest 30 minutes at room temperature.
Combine the vinegar, honey, pepper flakes, peppercorns, coriander, mustard seeds, fennel seeds, cumin and salt in a medium nonreactive saucepan over high heat and bring to a boil. Let boil for 2 minutes; remove from the heat and let sit until cooled to room temperature. Add the dill and cilantro. Place the cucumber in a medium bowl and pour the cooled vinegar mixture over them. Refrigerate, covered for 24 hours or up to 4 days.
Place 8 slices of bread on a work surface. Top each slice with 4 to 5 slices of the brisket, a slice of cheese and some of the red cabbage slaw. Top each with the remaining bread. Heat 1/2 of the butter in a large skillet over high heat. Saute 4 of the sandwiches at a time until golden brown on both sides and the cheese has melted. Serve with spicy pickles and chips.