Sprinkle the brisket liberally on both sides with 1 tablespoon salt and some pepper.
Place a large Dutch oven or heavy-based pot over medium-high heat. Add the oil. Add the brisket and sear on all sides until deep golden brown, 10 to 12 minutes. Remove the brisket and set aside. Add the garlic, celery, carrots and onions and cook until browned, about 5 minutes. Deglaze the pot with the wine and let simmer, about 1 minute. Then, use a wooden spoon to scrape the bottom of the pot. Then add the stock, rosemary, bay leaves and thyme. Add the brisket back to the pot fat-side up, cover and roast in the oven until the brisket is fork tender, about 3 hours.
Transfer the brisket to a cutting board and let it rest, about 15 minutes. Strain out the vegetables and skim off some of the excess fat and reserve the jus. Slice the brisket thinly across the grain.
Whisk the mayonnaise and mustard until well blended in a small bowl. Smear the top of the rolls with the mayonnaise mixture liberally. Place the mozzarella on the bottom of the rolls, pile high with the brisket and ladle the jus over top. Top with the Red Cabbage Slaw.
Red Cabbage Slaw:
Whisk the lemon juice, vinegar and sugar in a medium bowl. While whisking, slowly add the oil until smooth. Add the cherry peppers, shallots and cabbage. Taste and season with salt and pepper. Cover the bowl with plastic wrap and set aside in the refrigerator until you are ready to serve.