In a small bowl, whisk together the vinegar, 1/2 cup of oil, the mustard, Italian seasoning, paprika, salt, and pepper. Rub the marinade liberally on each chicken cutlet. Arrange on a quarter sheet pan lined with parchment paper. Cover with plastic wrap and freeze for 30 minutes. Chicken will freeze slightly. Remove from the freezer and with a sharp knife, chip the slightly frozen meat as thin as possible.
In a large saute pan over medium-high heat, add 2 tablespoons of oil. Add the onions and cook until slightly browned, about 2 minutes. Add the garlic and the chipped chicken meat and cook until the chicken is cooked through, about 5 minutes. Stir in the chives. Overlap the pepperoni on top of the chicken and repeat with the cheese slices. Turn off the heat and allow the heat from the meat to melt the provolone.
With the help of a spatula scoop up the chicken with the cheese and put it on the split roll. Tuck some cherry pepper spread on the side of the roll. Wrap tightly in a square of parchment paper. Repeat with remaining rolls and filling.