Step 1 Heat a grill, a broiler or a large skillet over high heat. Lightly brush the shiitakes with a little oil and season well with salt and pepper. Cook until tender. Sprinkle with the thyme and set aside to cool.
Step 2 Grill, broil or fry the steak until rare (if frying, use 1 to 2 tablespoons of oil).
Step 3While the meat cooks, slice the ciabatta lengthwise, leaving a hinge attached on one side and opening the loaf. As soon as the steak is done, lay it into the bread and season lavishly with salt and pepper. Spread with the chipotle chiles, then with the shiitakes. Fold over the top side of the ciabatta to close. Transfer the sandwich to a double layer of butcher's or waxed paper. Fold the paper over the sandwich and tie it with kitchen twine at 2-inch intervals. Wrap it with more paper. Place it on a baking sheet and weight it by placing a skillet or heavy cans on top. Refrigerate for at least 6 hours.
Step 4To serve, unwrap and slice off sandwiches as needed. Serve with a sharp cheese and chipotle mayonnaise, if you like.