For the hard-boiled eggs: Fill a large, deep saucepan with a tight-fitting lid with 2 inches of cold water.
Place the eggs in it and bring to a boil over medium-high heat.
Immediately turn off the heat and cover with the lid.
Let sit for 12 minutes.
Transfer to a colander and rinse under cold water.
Once cooled, peel the eggs and slice in half lengthwise.
Scoop out the yolks and place 4 yolks in each of 3 bowls.
Mash well with a fork.
Line a large serving platter with the greens.
For the pickles and capers: Add the mayonnaise, chopped capers, mustard and gherkins to one of the bowls of yolks and mash together until thoroughly incorporated.
Season with salt and pepper.
Divide the filling among 8 egg halves.
Top each with some capers and place on the platter.
For the wasabi and ginger: Add the mayonnaise and wasabi to the second bowl of yolks and mash together.
Season with salt and pepper.
Divide the filling among 8 egg halves.
Top each with a slice of pickled ginger and a small piece of cucumber and place on the platter.
For the sesame carrot: Add the mayonnaise, sesame oil, sesame seeds and carrot to the remaining bowl of yolks and mash together.
Season with salt and pepper.
Divide the filling among the remaining 8 egg halves.
Top each with more sesame seeds and place on the platter.