For the mushrooms: In a large bowl or a ziptop bag, whisk the olive oil, Worcestershire sauce, salt, pepper, garlic powder and lemon juice. Add the mushrooms and toss to combine. Marinate for 30 minutes to 1 hour.
For the onions: While the mushrooms marinate, make the onions. In a large skillet over medium high, heat the olive oil. Add the onions and saute until beginning to get tender, about 5 minutes. Season with salt and pepper. Reduce the heat to low. Cook, stirring occasionally, until the onions become a deep brown caramelized color, about 20 minutes. If they start to look dry or stick to the pan, add a tablespoon or 2 of water.
For the blue cheese spread: In a small bowl, mix the blue cheese and mayonnaise.
Heat a grill pan over medium-high heat.
Remove the mushrooms from the marinade and transfer to the grill pan. Cook until slightly wilted, browned and showing grill marks, 2 to 3 minutes per side.
For the sandwiches: Put the hoagie rolls on the grill pan until lightly toasted. Spread one side of each roll with the blue cheese spread. Top with some mushrooms, caramelized onions and arugula. Drizzle lightly with balsamic vinegar and a sprinkle of salt.