1. Salt the steak well and let it come to room temperature.
2. Dry sauté the mushrooms. Heat a large sauté pan on medium high heat. Add the mushrooms to the pan, as is (no butter or oil). Stir the mushrooms occasionally, and shake the pan a bit. You should hear the mushrooms squeak when they move in the pan. Continue to cook until the mushrooms release their moisture. Add a large pinch of salt and stir to combine.
3. Add the butter, rosemary and shallots. Stir to combine and sauté over medium-high heat for 2-3 minutes, stirring often. Pour in the red wine (you can substitute beef broth) and boil until the sauce has reduced by half. Turn off the heat.
4. While the mushrooms are cooking, prepare the grill for high direct heat. If you are using a gas grill, turn it on, cover it, and let it heat up for at least 10 minutes. (You want the grill to be very hot, which can difficult to do on a gas grill if the grill hasn't pre-heated long enough.) If you are using a charcoal grill, get the coals very hot. The grill is hot enough when you put your hand about an inch over the grill and you can only hold it there for 1 second. When the grill is hot, clean the grill grates with a wire scraper and then moisten a paper towel with vegetable oil. Using tongs, wipe down the grill grates with the oil-soaked towel.
5. While the grill is heating up, massage olive or other vegetable oil into the flank steak. You want the steak well coated. When the grill is hot enough, place the flank steak on a hot part of the grill. Sear for 4-6 minutes without moving. If you want a cross-hatch pattern of grill marks, about halfway through grilling, gently lift up a corner of the steak to check for grill marks, if you have them, pick up the steak with tongs and put it back down on the grill at a 90° angle (a quarter turn) from where it had been.
6. Turn the steak over. touch it to test for doneness (see the finger technique for checking for doneness). You might only need a couple minutes on this side, depending on how thick your flank steak is. Flank steak is best rare or medium rare; it becomes tough if it gets too well done. Try to undercook the meat just a little, as it will continue to cook a bit while it is off the heat resting. When the flank steak is almost done, take it off the heat and let it rest. Grind black pepper over it.
7. Finish the mushrooms. Turn the burner on high and boil down the liquids almost to a glaze. Add any meat juices that have accumulated with the resting flank steak. Taste for salt and add any if needed.
8. If you have a large steak, it may be easier to first cut it in half along the grain of the steak fibers. Then slice it thinly, on an angle, against the grain. Serve immediately with the mushrooms.