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Fill a medium saucepan with 2 inches water and bring to a boil, then reduce heat so water is barely simmering.
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Off the heat, whisk egg yolks in a heatproof bowl or on top of a double boiler until they become pale. Place over the simmering water. Whisking constantly, cook until the mixture is thick enough to hold a trail from the whisk and begins to hold its shape when drizzled from the whisk, about 3 minutes.
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Whisking constantly, add butter, 1 tablespoon at a time, whisking until each addition is incorporated completely before adding the next. When all the butter has been added, season with lemon juice, salt, cayenne, and black pepper. The sauce should be thick but still able to drizzle from a spoon (and it should form a pool, not a mound). If it is too thick, thin it with a little water.
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The sauce is best if used immediately but can sit for about an hour over hot water in a bain-marie or in a Thermos.
