In a small saucepan, combine the white wine vinegar, chopped shallots, and half of the tarragon. Let it simmer gently until the liquid reduces by half. This step concentrates the flavor and gives the sauce its signature depth.

Strain the mixture into a bowl and allow it to cool slightly. You want the flavor, not the chunks.

Fill a saucepan with a little water and bring it to a gentle simmer. Place a heatproof bowl on top, making sure it doesn’t touch the water. This indirect heat is key to preventing the eggs from scrambling.

Add the egg yolks and a tablespoon of water to the bowl. Start whisking continuously. After a minute or two, the mixture will become pale and slightly thick.

Slowly pour in the cooled vinegar reduction while whisking. This builds the base flavor of your béarnaise.

Now comes the most important step. Gradually add the melted butter in a slow, steady stream while whisking constantly. This creates the creamy emulsion that defines the sauce.

If the sauce starts to get too thick, add a few drops of warm water to loosen it.

Once all the butter is incorporated, remove the bowl from heat. Stir in the remaining tarragon, chervil, salt, and pepper. Add a small squeeze of lemon juice if you like a brighter finish.

Taste and adjust seasoning.