Heat 2-3 tablespoons of olive oil in a Dutch oven over medium-high heat.
Sear the venison roast until golden brown on all sides.
Transfer the roast to the slow cooker, leaving all the brown bits in the Dutch oven.
Turn the burner down to medium heat and add the beef broth. Using a wooden spoon, scrape up all the brown bits to deglaze the pan.
Pour the broth over the meat in the slow cooker.
Add the pepperoncini slices, along with the juices, the drained giardiniera, and all the spices.
Cook in the crock pot on low heat for 6 to 8 hours, or until the meat falls apart. Cook time can vary depending on the size of your venison roast.
Shred the cooked roast and add it back into the cooking liquids.
Toast the cut sides of the bread under a broiler for 3-4 minutes or until toasty brown.
Top the toasted buns with the shredded deer meat, including peppers and giardiniera. Put cheese slices on top of meat and place under broiler until cheese melts, approximately 1-2 minutes.
Serve with a small bowl of the braising liquid for dipping the sandwich.