1) Place a medium saucepan with the chopped shallot, white wine and vinegar over medium heat until it boils gently. Season with pepper and salt.

2) Let the liquid reduce fully. Then take the pan off the heat and let the cooked shallots cool for 5 minutes. Put the saucepan back over very low heat and then add the egg yolk.

3) Whisk vigorously to keep the yolk from scrambling. Keep the pan over very low heat and keep on whisking until the yolk sauce gets a sabayon like consistency.

4) One by one add small pieces of the cold butter to the pan and continuously move the butter around on a fork until it has fully melted. Then add another bit of butter. Keep the heat very low.

5) Keep stirring in bits of butter. The bearnaise sauce takes a while to come together. It needs to be done carefully so don't hurry. Add as much butter as you want. The sauce should have slightly thickened but still be light and creamy.

6) Stir constantly. Then check the seasoning in the end and add extra pepper or salt to taste. Add the chopped tarragon. Now turn the heat off and let the bearnaise sauce rest for another 2 minutes.

7) Transfer the bearnaise sauce to a jug and serve with freshly cooked steaks.