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Heat 1 tbsp of the oil in a small nonstick frying pan that has a lid. Tip the potatoes into the pan, cover and cook for 10 mins, shaking the pan occasionally so the potatoes get tossed around. Remove the lid and fry the potatoes uncovered for another 4-5 mins, until crisp and golden.
Meanwhile, season the steak. About 5 mins before the potatoes are ready, heat the remaining oil in a small heavy-based frying pan and fry the steak for 1½-2 mins on each side, depending how you like it done.
Take the steak out of the pan and put it on a warmed plate. Turn down the heat, spoon in the vinegar (it will evaporate immediately), then quickly stir in the crème fraîche and mustard and heat just until they melt and make a sauce. Sprinkle in most of the tarragon, stir and taste for seasoning. Pour the sauce over the steak and scatter with the remaining tarragon. Serve with the crisp potatoes and a green salad, pour yourself a glass of red wine – and tuck in.