In a medium bowl, finely chop eggs using a pastry blender or 2 forks, . Add mayonnaise, green onion, relish, mustard, dill, salt, and pepper, stirring until thoroughly combined. Cover and refrigerate until cold, approximately 4 hours.
Spread ΒΌ cup egg salad onto 4 bread slices. Top each with a remaining bread slice to make 4 whole sandwiches.
Using a serrated bread knife in a gentle sawing motion, trim and discard crusts from sandwiches to make even rectangles. Cut each sandwich into 3 finger sandwiches. Serve immediately, or cover with damp paper towels, place in a covered container, and refrigerate for a few hours until serving time.
Just before serving, garnish with paprika and cucumber slices and baby arugula.