Add the butter to a small saucepan and turn the heat as low as you can. This will melt the butter so slowly that the milk solids sink to the bottom and the fat will rise to the top.

After 10 minutes or so the butter will be completely melted. Turn off the heat and carefully pour the fat into a separate container. Use a spoon to carefully spoon off the last bit of fat. Discard the remaining liquid. You now have clarified butter. Set aside until needed.

In another small saucepan, add the shallots, white wine vinegar, white wine, 1 tablespoon of chopped tarragon, peppercorns, and lemon peel. Heat over medium until simmering, and then turn to low and cook until reduced by half.

Use a fine mesh sieve to strain out the solids, using the back of a rubber spatula to press out all the liquid. Discard the solids.

Bring a medium-sized pot with 1-½ inches of water to a simmer over medium heat.

Add the egg yolks and reduced liquid to a glass bowl large enough to sit on top of the pot of water without the bottom of the bowl touching the water. Place the bowl on the pot and whisk the egg yolks vigorously until they have thickened to a pale foam.

Remove from the heat and slowly add the clarified butter, while continuing to whisk vigorously. I like to place a damp towel or silicone pot holder under the bowl to help hold it in place while I do this.

The sauce will thicken as you whisk. If it becomes too thick, you can add a tablespoon or two of the hot simmering water. Be sure to whisk it as you add the water to avoid scrambling the eggs.

Once all the butter has been incorporated, add the remaining tablespoon of tarragon and salt to taste. Serve immediately.