Carefully remove the yolk from each egg and set the whites aside.
Add the yolks to a mini food processor.
Add the mayonnaise, mustard, horseradish, black pepper, and a few of the green onions to the yolks. Blend until completely smooth or as smooth as you like it.
Transfer the filling to a bowl and add the remaining green onions and capers. Stir well to combine.
Taste and adjust to your liking, adding more of whatever you like to suit your taste.
Fill the eggs and garnish with the remaining green onions.