Béarnaise Sauce
sauce veg

½ cup sherry vinegar
2 shallots, finely chopped
1 tsp cracked black peppercorns
1 bunch of tarragon, leaves only, finely chopped
1 extra sprig tarragon, for finishing, finely chopped
8 oz clarified butter
4 egg yolks, or more small ones
salt & pepper
Start clarifying the butter, if you haven't already but make sure you cool the butter off before using it! It should be warm but not hot - just hot enough to melt and turn clear but obviously less than 100°C.

In a small pot, combine the vinegar, shallots, cracked pepper and tarragon leaves. Bring to a boil and reduce until nearly dry. Remove from the heat and set aside.
If you prefer the sauce without the lumpy bits and don't want to strain the thickened final product, then sweat the aromatic ingredients and vinegar for a while with the lid tightly sealed, strain, return to the pot and then reduce.
You may add a teaspoon of water to loosen the contents again before adding it to the eggs for beating.
Place the egg yolks in a warm metal mixing bowl though glass worked perfectly well for me Add the tarragon reduction (and, if you're feeling cowardly and unambitious, a few drops of water to give a little insurance against curdling). Bring a few cups of water to a boil in the bottom half of the double boiler and place the metal bowl with the eggs over the simmering water. Whisk the eggs constantly, pulling the bowl away from the heat if the eggs start to curdle or harden.

Once the eggs have become very foamy and start to thicken, slowly begin to incorporate the clarified butter, whisking as you add it. (A tea towel "collar" can be useful to keep the bowl in place whilst you whisk.) Keep whisking. You're making emulsion here. Whisk until all the butter is incorporated. Season with salt and pepper and mix in the fresh choped tarragon sprig.
Serve immediately, or hold in a thermos (but not for longer than an hour).
This Béarnaise is just lovely

It seems using the same volume of chopped tarragon as shallots strikes the right balance.
I made half the quantity above, but probably doubled up the shallots, and used 3 rather small egg yolks.
If anything the sauce was a touch too thick - though I'm not sure how you'd go about preparing it thinner - with added water, fewer eggs, or just less vigorous egg whipping?

- Actually, maybe just make sure that the clarified butter isn't still really hot! But apparently the more water you add, the thinner the sauce will be.

On making a full quantity - although I did increase the amount of shallots, I think it might be best to do so cautiously. Stick closer to the quantities above - or you can make the sauce too sharp. Certainly don't overdo the vinegar.

If you curdle the bearnaise, say by overheating it with the butter, you can rescue it by whisking a fresh egg yolk in a clean bowl over the double boiler until it foams up, then gradually whisk the curdled bearnaise back in.