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.
Home-Made Pickles:
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.