Caramelize Onions and Mushrooms:

1. Prepare onions by cutting in half from root to end, peeling, and slicing into strips. Heat olive oil and 1 tablespoon butter in a sauté pan over medium-high heat.
2. Add mushrooms and cook for 2 minutes on each side until browned. Lower heat to medium-low, add the remaining butter and onions, and cook uncovered for 30-45 minutes, stirring every 5 minutes, until onions are translucent and caramelized. Deglaze with ¼ to ⅓ cup water, scraping up browned bits. Add salt and optional sugar to taste.

Make Roasted Red Pepper Aioli:

1. Mince garlic cloves and combine with kosher salt. Add garlic paste, mayonnaise, lemon juice, olive oil, diced roasted red peppers, and cayenne pepper to a blender or food processor. Blend until smooth.

Cook Steak and Rolls:

1. Preheat the grill over high heat. Brush steaks with olive oil and season with salt and pepper. Cut ciabatta rolls in half and butter the insides.
2. Grill rolls butter side down for 3 minutes until toasted. Grill steaks for 30-45 seconds per side. Let steaks rest, then slice across the grain.

Assemble Sandwich:

1. Spread aioli on both halves of the rolls. On the bottom half, layer steak slices, caramelized onions and mushrooms, and provolone cheese. Return to the grill for about 2 minutes, or until cheese melts. Top with arugula and place the other half of the roll on top.

Serve:

1. Cut sandwiches in half if desired and enjoy!