Satsuki's sandwiches (My Neighbor Totoro)

Steps

1. Cook the eggs in a small saucepan of simmering water until the yolks are set but still soft, then cool them in cold water until the shells peel off easily.
2. Peel the eggs, roughly separate the whites and yolks, then mash with a fork along with the mayonnaise, mild mustard, salt, white pepper, and sugar until you get a thick spread with tender little pieces.
3. Slice the cucumber very thinly, salt it lightly, let it release its water until it becomes soft and shiny, then blot it thoroughly so it doesn't make the bread soggy.
4. Spread a thin layer of softened butter on each slice of bread, going right to the edges to create a moisture barrier.
5. Assemble a portion of the sandwiches with an even layer of the egg salad, then close them without pressing down hard, to keep the bread fluffy and soft.
6. Assemble the rest of the sandwiches with the ham folded flat and the drained cucumber slices, then close them, aligning the edges.
7. Wrap the sandwiches in plastic wrap or a clean kitchen towel and let them rest in the fridge until the filling sets and the slices adhere without being squashed.
8. Remove the crusts if necessary using a long, sharp knife, then cut into neat triangles just like for a family bento.
9. Serve cool but not ice-cold, on a ceramic plate, with the cut sides visible and the crumb still soft to the touch.