Preheat the oven to 300 degrees F.
Heat the oil in a Dutch oven over medium-high heat until almost smoking.
Rinse the chuck roast and pat dry with paper towels. With a sharp knife, make 10 to 12 deep slits in the roast large enough to hold a clove of garlic. Insert a clove of garlic into each slit so that it is completely embedded.
Rub the roast with a little salt and pepper, then place into the hot oil. Sear on all sides until brown and crusty. Spread the roast with the hot sauce. Pour the beef stock and 1 cup water into the bottom of the pot and cover with the lid.
Transfer to the oven and cook until the roast is falling apart, 3 to 3 1/2 hours. Using two forks, shred the meat in the pot. Set aside to keep warm.
Raise the oven temperature to 425 degrees F. Cut the rolls in half and spread with mayonnaise on both sides. Place a generous portion of the shredded meat on the bottom half of each roll. Set the bottoms on a baking sheet and top each with a small amount of the provolone. Transfer to the oven to melt the cheese, 2 to 4 minutes.
Remove the rolls from the oven and top each with pickles, tomatoes and shredded lettuce. Cover with the roll tops to make sandwiches. Serve immediately.