Thanks to Greensbury Market for the chuck roast that inspired this recipe.
Set the EGG for direct cooking without the convEGGtor at 450°F/232°C.
Season the roast with salt and pepper. Place the meat in the EGG and sear on all sides until browned but still very rare. Remove the roast from the EGG and set it aside.
Set the EGG for indirect cooking with the convEGGtor at 300°F/149°C.
Place the roast in a Big Green Egg Dutch Oven along with the beer, beef broth, onion, and pepperoncini with juice.
Cover the Dutch Oven, add to the EGG, and cook for 5 hours. After 5 hours, remove the Dutch oven from the EGG and set it aside. Shut down the EGG by closing the top and bottom vents.
Let the meat rest in the Dutch Oven (covered) for 1 hour; then shred the beef in the juices. Add beef to a split hoagie roll and add smoked provolone cheese to the top. Place the sandwich on the grid and use the residual heat of the EGG to melt the cheese; approximately 3 minutes.
Use the juice from beef for dipping the sandwich. Top with fried option as an option. Enjoy!