Brown butter gives this sauce a nutty, roasted flavor, a big leap forward from standard white béarnaise. At Alfred's Steakhouse in San Francisco, the cooks use a whipped-cream siphon to turn the sauce into a velvety cloud.
In a small saucepan, heat vinegar, tarragon, and peppercorns over medium-high heat until reduced by half, about 5 minutes. Strain into a small bowl and let cool.
While vinegar is reducing and cooling, heat butter in a medium saucepan over medium-low heat until foam has mostly subsided and butter is the color of honey, 25 to 35 minutes. Strain through a fine-mesh strainer. Let cool to very warm but not scalding.
In a blender, blend egg yolks, 1 tbsp. vinegar reduction, and a pinch of salt on low speed. With blender running, in a thin stream (the width of spaghetti), pour in half of hot brown butter; then pour in the rest more quickly. Add 2 tsp. lemon juice, then 1 to 3 tbsp. cold water as needed to keep blender moving.
Taste and season with salt. To keep sauce warm up to 2 hours, pour into a metal bowl and nestle in a pot of steaming (not boiling) water, or aerate in a 1-pint whipped-cream siphon*, following manufacturer's instructions (sauce will stay warm and fluffy).
*The sturdy iSi Gourmet Whip whips both cold and hot mixtures ($150; a pack of 10 iSi cream charger cartridges, $15; williams-sonoma.com).
Make ahead: In bowl, up to 1 day ahead, chilled airtight; rewarm in a hot water bath as described above, whisking to loosen.
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