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.

Preheat a sauté pan or large skillet over medium-high heat. Add olive oil and 1 tablespoon of butter until the butter is melted.

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.

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.

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.

While the onions are caramelizing, make the aioli. Finely mince garlic cloves or smash them through a garlic press. Place on a cutting board.

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.

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). You don't have to be gentle with it, since you'll be pureeing it anyway.

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.

When the onions have about 15 minutes left to caramelize, preheat your grill over high heat for about 10 minutes.

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.

Cut the ciabatta rolls in half and butter the insides.

When the grill is hot, add the rolls butter side down on the grill warming rack (that little grate above the main grill). If you don't have a warming rack, turn down one burner to medium heat and place the rolls on that side of the grill. Cook for about 3 minutes until lightly toasted and golden brown.

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 but don't turn if off yet.

Let the steak rest for a couple minutes (it doesn't need long because it's so thin) before slicing across the grain with a sharp knife. Toss the steak slices in any remaining juices.

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 and then put the bottom halves of the sandwiches back on the grill for about 2 minutes, or until the cheese is melted. (You can turn off the grill now)

Add a handful of arugula on top of the melted cheese and place the other half of the bun (sauced) on top.

Cut sandwiches in half, if desired, and enjoy the heck out of it!!