While the steaks are resting, either use the same cast iron pan or a non-stick pan to melt the butter. Oil will also work, but should be kept cooler than for searing the steaks. Make sure the mushrooms are well washed and cut into quarters or broken into quarter-sized pieces
Let the butter get to the beginning of the browning process, then add the mushrooms. Sprinkle the salt on and keep the heat on medium to keep the moisture cooking out of the mushrooms. Stir them once every few minutes to prevent sticking or burning, watching for the oil or butter getting too hot.
Cook until the mushrooms are soft and well-browned, then add the dried or fresh tarragon and the green onions. Stir it in and let the mixture continue cooking until the juices in the pan thicken slightly
Spoon the hot mushrooms and their juices over the steak and serve immediately