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Mix the mayo with the mustard and set aside. Season the steaks. Heat a drizzle of oil and the butter in a large frying pan over a high heat until sizzling and turning nut brown. Cook the steaks for 1-2 mins on one side, then turn and cook for another 1-2 mins. Turn again and continue this process for 6-7 mins total for rare, 8-9 mins for medium- rare and 10 mins for medium. Turning the steaks helps them cook evenly and build a uniform crust.
When the steaks are cooked to your liking, transfer to a board and leave to rest. Meanwhile, cook the sauerkraut in the pan with the sticky steak juices for 3-4 mins until heated through and browned. Serve the steaks with the sauerkraut and the mustard mayo on the side, or spoon the sauerkraut over the steaks.