Place butter in a microwave safe bowl and microwave for 15 seconds. Butter should be just melted- it's okay if there are a few chunks that aren't totally melted. Stir until it is an even consistency and set aside to cool a bit.
In a deep bowl or measuring cup, add the egg yolk and lemon juice and blend together with a hand blender until well combined.
When the butter has cooled off enough to coat the back of a spoon, add it to the bowl with the egg yolk and lemon juice and use the hand blender to mix until well combined. Use immediately. The sauce will continue to thicken as the butter comes back to room temperature.
Notes
LeftoversSauce is best consumed immediately after preparing. However, it can be stored in an airtight container in the refrigerator for up to 2 days. Warm over low heat, stirring constantly, until desired consistency is reached.