For the rolls: Preheat a grill or grill pan to medium-high heat.
Halve the rolls horizontally and remove some of the bread from the insides of the top halves. Drizzle the rolls evenly with the olive oil and grill until lightly toasted, 2 to 3 minutes. Remove to a tray and rub the toasted sides of the rolls with the garlic. Set aside.
For the filling: Sprinkle the steak evenly on both sides with 1 teaspoon salt. Drizzle the onion slices with 1 teaspoon olive oil and sprinkle with the remaining 1/2 teaspoon salt, being careful to keep the slices intact so that they are easier to grill. Place the steak and onions on the grill and cook until an instant-read thermometer inserted in the steak reads 135 degrees F and the onions are deep golden, 5 to 6 minutes per side. Allow the steak to rest for 10 minutes before slicing.
Meanwhile, combine the olives, basil, sun-dried tomatoes, capers, lemon juice, anchovy paste, oregano, roasted peppers and remaining 2 tablespoons olive oil in a large bowl. Mix well to combine. Thinly slice the steak against the grain. Add the sliced steak to the filling, along with the grilled onions and any accumulated juices from the plate. Toss well to combine.
Place two slices of provolone on each toasted roll. Fill each roll with 1 cup arugula. Divided the steak filling among the rolls. Cut them in half and serve.