Place the egg, lemon juice, mustard, and salt in a tall, narrow container.
Pour the oil on top and let the mixture settle for a few seconds.
Insert an immersion blender all the way to the bottom and turn it on.
Blend without moving the blender until the mixture starts to emulsify.
Slowly lift the blender to incorporate the remaining oil until smooth and creamy.
Taste and adjust seasoning as desired.