There was a time when the wealthy had greenhouses and could grow plants. Therefore, they could make delicacies any time of the year. The tarragon and chervil were always available. I can get chervil at the Farmer's Market only when the weather cooperates.
I ran a netsearch on Béarnaise sauce and the citations returned are all a monotone. Martha Stewart's is the same as Epicurious', as Ina Garten's, as New York Times'. The guy at the Food Lab gets closest to the original.
There may be another reason that this sauce is no longer made and I'm again guessing it is too much work. But haute cuisine is worthy of re-creating. So here goes.
Words in brackets are mine.
Larousse Gastronomique. Page 817.
1 tbs. chopped shallot
2 tbs (3 tbs) tarragon and chervil [sic]
a sprig of thyme
a fragment of bay leaf
3 tbs vinegar
3 tbs white wine
1 pinch of salt
1 pinch of mignonette pepper
2 egg yolks
1 tbs water
1 tbs water
4 ozs butter
a squeeze of lemon juice
a pinch of cayenne pepper
1 additional tbs of tarragon, garnish
1 additional tbs of chervil, garnish
None of the above recipes from these experts use the cayenne or bay leaf. My guess about the tarragon-chervil confusion is 2 T tarragon and 1 T chervil. But my instincts would prefer 2 T chervil. Your guess?
I'm giving the instructions in a proper order.
Take the butter from the frig and set on the counter to come to room temp. Chop the tarragon, cover and reserve. Chop the chervil, cover and reserve. Peel and chop the shallots. Reserve. Crack the eggs and separate the yolks. Reserve the yolks. Save the whites for other uses. Cut the lemon for convenient squeezing. In a mortar, crush the pepper.
In a small saucepan, put the wine and vinegar. Add the tarragon, chervil, thyme and bay leaf. Season with the salt and a pepper. Reduce by ⅔, remove from heat and bring to room temperature. Mix the yolks with the 1 tbs water. Whisk the sauce over very low heat. As soon as the eggs begin to thicken the sauce, stir in the butter in ½ inch cubes, one or two at a time, whisking continuously.
Season the sauce [add more salt if needed], sharpen the sauce with lemon juice and cayenne. Strain. Finish off with the tablespoons of chervil and tarragon. Keep warm in a double-boiler.
Cooks Note: the wine vinegar reduction of 3 fluid ounces becomes, when reduced 1 fluid ounces. There is a spelling error in the Larousse Index. Under the Sauce category the spelling of the sauce is Barnaise.