Season chuck roast with salt and pepper on both sides. Heat 1 tablespoon oil in a Dutch oven or large pot over medium-high heat. Sear chuck roast until browned on both sides. Remove beef and set aside.
Heat remaining tablespoon oil in the same pot. Add onion and garlic and saute until softened, about 5 minutes. Add ginger, star anise, bay leaves, and Shaoxing wine and bring to a boil.
Add back chuck roast along with star anise, bay leaves, soy sauce, oyster sauce, sugar, and beef broth. Bring to a boil, cover the pot, and transfer to the oven. Continue to braise for 2 hours or until beef is tender and shreds easily with a fork.
Remove beef from braising liquid and shred with 2 forks. Strain braising liquid, discarding aromatics but setting aside onions. Use a fat separator to skim the fat from the braising liquid and keep warm.
Increase oven temperature to 400 degrees F.
Slice hoagie rolls in half and place on a baking sheet. Top bottom half with shredded braised beef and reserved cooked onions. Place two slices of cheese on top and place in the oven for 2-3 minutes or until cheese has melted. Remove from oven and place remaining hoagie roll on top. Serve with braising liquid on the side for dipping.
Notes
If preparing the sandwiches ahead of time, braise the beef the day before and spoon a couple of tablespoons of the braising liquid on top. Before assembling the sandwiches, reheat the beef, cooked reserved onions, and the braising liquid.