In the bottom of a 6 quart slow cooker combine the beef stock, giardinieara mix, Italian seasoning, garlic, peperoncinis, and peperoncini juice.
Heat a heavy bottom skillet over medium heat. Add the olive oil and heat until the oil just begins to smoke.
Season the chuck roast with salt and pepper on both sides. Add it to the hot skillet and brown for about two minutes on all sides. Then transfer to the slow cooker.
With the heat still on the skillet, add the red wine and using a wooden spoon, pull up the pan drippings. After about 30 seconds, add the liquid from the pan to the slow cooker. Cook on low for 8 hours.
Cover the slow cooker and cook on low for 8 hours. (See the post for information on cooking on high.)
Remove the beef from the slow cooker and shred with two forks. Return the shredded beef to the crock pot.
The shredded beef can be added to rolls and served.
If you would like to have cheese on your Italian beef, butter the inside of the rolls. Add the beef, top with cheese, and put under a broiler watching very closely so it does not burn.