Place the egg yolk and lemon juice in a blender or food processor and pulse to combine. Put the butter into a small saucepan or Pyrex measuring cup and heat on the stovetop or in the microwave until melted and hot. With the motor running, slowly pour the butter into the blender through the feed tube (or hole in the lid) until it's all incorporated and the mixture is slightly thick. Grind in some black pepper, add the cheese and pulse to combine.
Serve soon (it will solidify once refrigerated).