Salt and pepper beef & saute in oil over medium to high heat, browning all sides. Remove beef & set it aside.
Saute celery, carrot onion & garlic in the pan used to brown the meat until slightly browned. Add ½ cup of beef stock and stir to deglaze the bottom of the pan.
Add sliced pepperoncini, return the beef to the pan & add more beef stock until it covers about ½ of the beef.
Add giardiniera & juice, bring the liquid to a simmer, cover & place in a 350 degree oven for 30 minutes or until the internal temperature reaches 125-135 degrees.
Remove beef to a separate plate and refrigerate to make it easier to slice in next step. Transfer the stock & vegetables to a sauce pan & bring to a low simmer to reduce it a bit and concentrate the flavors.
Slice the cool beef across the grain as thinly as possible & slice the rolls ¾ of the way through horizontally.
Just prior to serving, take enough of the sliced beef to fill a sandwich & dip it into the simmering broth for 3 or 4 seconds then transfer it directly to one of the rolls. Add some of the vegetables & some broth to the top of the sandwich, close the sandwich and roll it in a piece of parchment paper. Let it sit for at lease a few moments so that the flavors can expand throughout the sandwich then cut and serve.