Strip the tarragon leaves from the stem and chop into small pieces.
Put 2 tablespoons of soft butter into a bowl and mash with a fork. Add half of the chopped tarragon and mix well.
Scrape the butter together and place on a piece of cling film. Form it into a sausage shape and twist the ends to seal. Place in the freezer for 10 minutes to firm up.
Unwrap the butter and roll in the remaining chopped tarragon. Leave in the fridge until needed.
Bring the meat to room temperature 30 minutes before cooking. Remove the meat from the packaging and pat dry with kitchen paper.
Rub a tablespoon of butter over both sides of the steaks and season both sides with salt and pepper.
Heat the oil over a medium to high heat in a large frying pan. Add the steaks and cook for 3 minutes.
Turn the steaks over and cook for a further 3 minutes, then add the remaining tablespoon of butter to the pan and baste the steaks.
Remove from the heat, cover loosely with foil, and leave to rest for a few minutes.
Serve the steaks with a slice of tarragon butter and the buttery juices from the pan poured over.