Separate the mushroom stems from caps. Chop mushroom caps into thirds.
Remove tarragon leaves from stems; discard the stems.
Season the steak with salt and pepper on both sides.
Heat a heavy frying pan over high heat. Once very hot (a drop of water should immediately sizzle and evaporate when flicked onto the pan's surface), add a generous drizzle of oil. Add the steak and cook for 4 minutes, turning once.
Remove the steak from the pan and set aside. Tent with foil to keep warm. Discard the oil remaining in the pan.
Reduce the heat and add the garlic, shallot and mushrooms to the frying pan. Cook till softened, stirring frequently to prevent burning.
Add white wine to the frying pan and cook till reduced slightly, then add beef stock. Reduce heat to low and begin adding butter, one piece at a time. Stir well between each addition. Finally, add the tarragon and stir well.