Pull meat out of the fridge and let rest for 20 to 30 minutes.
Heat oil in a large skillet set over medium-high heat.
Add the beef chunks to the hot oil and sear for about 4 minutes per side, or until browned.
Transfer beef to the insert of your slow cooker.
Return skillet to the burner.
Add a splash of beef broth and, using a wooden spoon, scrape up all the browned bits from the bottom of the skillet. Cook for 1 minute.
Remove from heat and pour the liquid over the beef in the slow cooker.
Sprinkle the packet of Italian Dressing Mix over the beef.
Add the pepperoncini peppers, pepperoncini juice, and giardiniera.
Season with italian seasoning and pour in the remaining beef broth.
Cover and cook on LOW for 8 to 10 hours, or until meat is fall apart tender. You can also cook it on HIGH for 5 to 6 hours.
Remove beef from the slow cooker and transfer to a cutting board; shred it.
Return the shredded beef to the slow cooker; cover and cook for 20 minutes.
Serve the shredded beef on toasted buns with provolone and giardiniera.