Finely chop the shallots and tarragon.

Crush the peppercorns.

Combine shallots, 1 tbsp tarragon, white wine vinegar, white wine, and crushed peppercorns in a heavy nonreactive saucepan.

Bring the mixture to a boil over high heat.

Boil for about 2 minutes, or until the mixture has reduced by half.

Strain the liquid through a sieve and let cool slightly.

Whisk the egg yolks and 1 tbsp water in a heatproof bowl.

Place the bowl over a saucepan of barely simmering water (double boiler).

Whisk in the cooled liquid reduction into the egg yolks.

Whisk in the butter, 1 tbsp at a time, until each addition softens into a creamy sauce before adding more.

Whisk in the lemon juice and remaining tarragon.

Season with salt and pepper to taste.

Serve immediately.