Fill a medium pot halfway with water, bring just to a boil over medium high heat, then carefully add the eggs. (The water should just cover them. Add more, if necessary.) Reduce heat to just below a simmer and cook eggs for 20 minutes. Drain and rinse eggs with cold water to stop the cooking process, then shell them when cool enough to handle.

Mash, grate, or chop the eggs (grating makes for a fluffier texture) and transfer them to a medium bowl. Add mayonnaise, relish, green onions, mustard, salt and pepper and mix well. Cover and chill egg salad in the refrigerator for at least 1 hour.

Divide egg salad between 6 slices of bread and spread out evenly with a knife. Top with remaining slices of bread and press each sandwich down lightly. Using a large cookie cutter (any shape you'd like), cut out the sandwiches and transfer to a platter. Cut the remaining part of each sandwich into geometric shapes and transfer to the platter, if you like.

Serve immediately, or cover platter with a slightly dampened paper towel and plastic wrap, then refrigerate until ready to serve.