Special equipment: a grill pan
For the mushrooms: In a small bowl, mix together the oil, steak seasoning, Worcestershire sauce and some salt. Brush the mixture on both sides of each mushroom and set them aside to marinate a little while you preheat your grill pan.
Heat a grill pan over medium-high heat. Add the mushrooms top-side down and cook until tender, about 3 minutes on each side, topping each mushroom with a slice of cheese when it has 1 minute left on the second side; let it melt. If needed, cut the mushroom to make sure it will fit your bread nicely.
Meanwhile, in a bowl, stir together the mayonnaise, chives, mustard, a small pinch of salt and some black pepper. In another bowl, toss together the arugula, salt, pepper and some olive oil.
Place a dollop of the mayo mixture on one side of 1 of the slices of bread. Top with a mushroom and some dressed arugula, then place another piece of bread on top, give it a gentle press and cut in half. Repeat with the remaining ingredients.