In a large pot, combine the white vinegar, water, red pepper flakes, salt, sugar, and garlic and bring to a boil over medium heat. Once boiling, remove the pot from the heat and add the sliced peppers and onions. Let the ingredients pickle at room temperature for about 30 minutes. The peppers will last up to 1 month in a re-sealable container that has been stored in fridge.

Preheat an outdoor grill or grill pan over medium-high heat. Arrange the butterflied sausages on the grill, cut side down. Cover the sausages with a sheet pan and weigh it down with a tea kettle filled with water or a heavy pan. Grill for 4 to 5 minutes per side.

Slice the rolls in half and brush them, inside and out, with the olive oil. Layer a slice of provolone over the bottom half of each roll. Add the cooked sausages to the cheese, top with some of the pickled peppers and onions, then finish with 3 pieces of shaved Parmesan and, finally, cover with the top half of each roll. Put the sandwiches in a panini press, 2 or 3 at a time, and cook until the bread is crisp and cheese is melted, about 4 to 5 minutes. If you do not have a panini press, grill the sandwiches in a large skillet over medium heat and put a cast iron or heavy-bottomed pan on the sandwiches to flatten. Cook for 3 minutes per side. Transfer the sandwiches to a serving platter and serve.