Melt the butter in a skillet over high heat. Add the mushrooms and cook, stirring every minute or so, until the mushrooms release their water and brown, 4 to 5 minutes. When finished, remove from the heat and mix in the creme fraiche, dill and chives.
Cover another skillet with coarse salt and turn to high heat. Grill the steak until browned, or to your liking. Remove from the heat and cut into strips. Top the steak with the mushrooms and serve.