Melt the butter and heat it carefully until the whey residue sinks to the bottom and the butter is clarified. Separate the fat from the whey and keep warm.
For the reduction peel the shallot and cut it into fine cubes. Crush the peppercorns with the back of a knife or in a mortar. Bring vinegar, 2 tablespoons of water, peppercorns and diced shallots to the boil in a small pot and reduce to 1/3 liquid.
Pour reduction through a sieve into a stainless steel bowl.
Add 1 tablespoon of water and egg yolks and whisk. Whisk over a hot water bath (60-70 °C) with a whisk until a creamy mixture is formed. Gradually beat butterfat drop by drop into the egg yolk mixture.
Season to taste with lemon juice, salt and ground white pepper.
Cut the avocado in half, remove the core and peel the flesh. Dice approx. 1/4 of the flesh, puree the rest. Stir the fruit flesh into the hollandaise sauce, except for a few cubes for sprinkling.
Arrange and sprinkle with avocado cubes.