For the butter, put all the ingredients into a mixing bowl and combine with a wooden spoon until smooth. Spoon onto some cling film, then roll into a log about 5cm in diameter. Place in fridge until firm, then cut into 1/2cm slices. Put aside enough sliced butter for 4 slices, placing each slice on a square of baking paper. The butter needs to be at room temperature so it melts easily on the steak.
Return the remaining butter to the fridge or freezer for later use. If freezing, place a small piece of baking paper in between each slice so you can use it, slice by slice, as and when you need it.
Cut beef crosswise into four steaks. Place each slice between 2 sheets of cling film and pound, one by one, until very thin (about 5mm). Remove cling film and season beef with sea salt and black pepper, then drizzle lightly with oil.
Preheat a chargrill or frying pan on a high heat. Cook each piece of beef for about 1 minute on one side (until browned), then turn and cook for another 10 seconds – they should still be juicy and pink in the middle. Remove from heat, cover with foil and rest for a minute.
Place a slice of softened butter onto the cooked minute steak and serve immediately with fresh lime.