For the caramelized onions and mushrooms
1-Prepare onions: Prepare onions. Cut in half from root to end and peel off papery skin. Quarter and remove the core. Then slice in strips about 1/4″ wide from root to end.
2-Preheat a sauté pan or large skillet: Preheat a sauté pan or large skillet over medium-high heat. Add olive oil and 1 tablespoon of butter until the butter is melted.
3-Add mushrooms in a single layer and: Add mushrooms in a single layer and sprinkle with a little salt. Cook for 2 minutes, then flip and cook an additional 2 minutes to get some brown on the edges of the mushrooms.
4-Lower the heat to medium low and: Lower the heat to medium low and add remaining butter and onions. Cook uncovered for 30-45 minutes, stirring every 5 minutes or so, until onions are floppy, translucent, and caramel colored. Add a little butter if the mixture starts looking dry.
5-Deglaze with about 1/4 to 1/3 cup: Deglaze with about 1/4 to 1/3 cup of water, scraping up any fond that has formed on the bottom of your pan. Add salt to taste and, if desired, a little sugar to bump up the sweetness a bit.

For the roasted red pepper aioli
6-Finely mince garlic cloves or smash them: Finely mince garlic cloves or smash them through a garlic press. Place on a cutting board.
7-Add kosher salt and smash together with: Add kosher salt and smash together with the garlic with the flat of a chef’s knife, scoop it into a pile, and smash it again until it forms a relatively smooth paste.
8-Dice the roasted red pepper and place: Dice the roasted red pepper and place in a paper towel or clean kitchen towel. Squeeze out any excess liquid (otherwise your aioli will be runny).
9-Add garlic paste, mayonnaise, lemon juice, olive: Add garlic paste, mayonnaise, lemon juice, olive oil, roasted red peppers, and cayenne pepper to an immersion blender cup or the bowl of a mini food processor. Blend until smooth.

To cook the steak and rolls
10-Preheat your grill over high heat for: Preheat your grill over high heat for about 10 minutes.
11-Brush both sides of the steak with: Brush both sides of the steak with a little bit of olive oil (not too much or the grill will flare up), and sprinkle with kosher salt and freshly cracked black pepper.
12-Cut the ciabatta rolls in half and: Cut the ciabatta rolls in half and butter the insides.
13-Add the rolls butter side down on: Add the rolls butter side down on the grill warming rack. Cook for about 3 minutes until lightly toasted and golden brown.
14-Place steaks on the grate over a: Place steaks on the grate over a hot burner. Cook for about 30-45 seconds, flip, and cook for another 30-45 seconds before removing to a plate. Turn the grill down to medium-low heat.
15-Let the steak rest for a couple: Let the steak rest for a couple minutes before slicing across the grain with a sharp knife. Toss the steak slices in any remaining juices.

To assemble the sandwich
16-Spoon two tablespoons of aioli on each: Spoon two tablespoons of aioli on each side of the roll. On the bottom half of the roll, pile on 1/4 of the steak slices and 1/4 of the caramelized onions and mushrooms. Add two slices of provolone.
17-Put the bottom halves of the sandwiches: Put the bottom halves of the sandwiches back on the grill for about 2 minutes, or until the cheese is melted.
18-Add a handful of arugula on top: Add a handful of arugula on top of the melted cheese and place the other half of the bun (sauced) on top.
19-Cut sandwiches in half, if desired, and: Cut sandwiches in half, if desired, and enjoy.