Hard boil six eggs. Let eggs cool, then peel and cut the eggs in half, saving one yolk for garnish. Wash each egg white in cold water to remove any remaining yolk. Dry egg whites on a paper towel with the cut side down for a least five minutes.
Combine remaining egg yolks, mayonnaise, Dijon mustard, salt, water, verjus and Worcestershire sauce in food processor and blend until smooth.
Transfer mixture to a bowl and fold in sieved egg white, capers, cornichons and shiitake mushrooms. Put mixture into a piping bag.
Turn cut egg whites so the cut side faces up and lightly season with kosher salt. Pipe yolk mixture into the egg white until even with the top. Garnish the top of the egg with sieved egg yolk and porcini powder.