Boil the potatoes with the skin on, peel, and mash them.
Boil the eggs, peel, and chop them finely.
Place the mashed potatoes and eggs in a bowl, season with salt and pepper.
Put the potato and egg filling on one slice of bread, then cover with another slice.
Melt butter in a pan and grill the sandwich on both sides until golden brown.
Cut into bite-sized pieces.