Make hollandaise sauce: In the bottom of a double boiler or in a medium saucepan, bring 1 in. of water to a simmer over high heat and adjust heat to maintain simmer. Put egg yolks, lemon juice, and mustard in top of a double boiler or in a round-bottomed medium bowl and set over simmering water. Whisk yolk mixture to blend.

Whisking constantly, add butter in a slow, steady stream (it should take about 90 seconds). Cook sauce, whisking, until it reaches 140°, then adjust heat to maintain temperature (remove from simmering water if necessary). Add salt and pepper and continue whisking until thick, about 3 minutes. Adjust seasonings to taste. Remove from stove and set aside.