Preparation

• Heat the oil in a 10-inch heavy skillet (preferably cast iron) over medium-high heat until very hot but not smoking. Season the steak on both sides with the salt-and pepper. Put the steak in the hot oil and sear for 3 minutes. Turn the steak and cook for another 2 minutes (it will be very rare but will cook more later). Take the skillet off the heat, transfer the steak to a cutting board, and cover loosely with foil.
• Return the skillet to medium heat. Add the mushrooms and onion and cook, stirring occasionally, until they’re tender and beginning to brown, about 5 minutes. Add another 1 Tbs. canola oil if the pan seems dry. Add the scallions and garlic and cook until the scallions are limp, about 1 more minute. Loosely cover the skillet and slide it off the heat.
• Trim the fat from the side of the steak and cut the steak into thin (1/8- to 1/4-inch) slices. Add the steak slices, any accumulated juices, and the tomatoes to the mushrooms in the pan; season with salt and pepper and toss well. Divide into two loose piles in the skillet. Lay a cheese slice over each pile; cover the skillet to melt the cheese (briefly set the skillet over low heat, if necessary). Slide a large metal spatula under one pile of steak, mushrooms, and cheese and drape it over the toasted bread; repeat with the other pile. Serve immediately.

Serve a little carrot salad or Buttermilk & Herb Slaw on the side, if you like.