Chef John's Ultimate Steak Sandwich

Ingredients (14)

• + 1 (2 pound) fully-trimmed flat iron steak add to pantry
• + salt and pepper add to pantry
• ✓ 8 ounces brown clamshell mushrooms, grilled, separated
• + salt and pepper to taste add to pantry
• + salt and pepper to taste add to pantry
• + 1 tablespoon sherry vinegar add to pantry
• + 2 tablespoons extra virgin olive oil add to pantry
• + 3 tablespoons barbeque sauce add to pantry
• ✓ 2 tablespoons vegetable oil
• + 1 tablespoon cider vinegar add to pantry
• + 6 hot dog buns add to pantry
• ✓ ½ cup mayonnaise, or as needed
• + 1 cup arugula leaves, or as needed add to pantry
• + 1 cup quartered cherry tomatoes add to pantry