Put the shallots and pepper corns in a pan.
Add half the tarragon, then the vinegar and white wine.
Bring to a gentle heat and reduce until the mixture is has nearly evaporated.
Meanwhile, add the water to another saucepan and bring to a gentle boil.
Melt the butter in a bowl over the water and turn off the heat.
Add two tablespoons of water to the tarragon and vinegar mixture.
Add the egg yolks.
On a gentle heat, whisk the mixture into the consistency of a sabayon (thick and mousse like), ensuring the heat is no higher than 60°C.
Remove from the heat and add the melted butter one ladle at a time (ideally at a temperature of 40°C). Season the sauce.
Pass the mixture through a muslin cloth into a bowl to keep the consistency smooth.
Add the remaining fresh herbs, season with salt and mix thoroughly.
Serve the béarnaise with your favorite cut of steak.