Put a frying pan over a high heat and add the butter. When hot and the butter is bubbling, add the steaks and fry for 2 minutes then turn over and fry for a further 2 minutes.
30 g unsalted butter
Remove the steaks and keep warm for now.
Add the shallot with the white wine vinegar and about ½ of the tarragon.
1 large shallot, 50 ml white wine vinegar, 1 bunch tarragon
Bring up to a boil and remove from the heat. Using a fine sieve, drain the contents of the pan keeping the liquid. This is homemade tarragon vinegar.
Place a saucepan of water over a high heat and bring to a boil. When boiling reduce to a simmer and place a bowl over the pan but not touching the water.
Add the egg yolks, lemon juice and the tarragon vinegar and gently whisk together.
3 large egg yolks, 1 medium lemon
Slowly add the clarified butter whisking constantly until it thickens.
200 g unsalted butter
Finely chop the remaining tarragon and place in the sauce and continue to stir.
1 bunch tarragon
Place the warm steaks and their juices onto plates and spoon over the bearnaise sauce. Add a salad, roast potatoes, chips or whatever you prefer.