Add whatever fresh herbs you like here to vary the flavor profile. A sprinkling of paprika makes for a pretty presentation. I also like to stir in sriracha or pesto for a variation.
Place the eggs in medium saucepan, cover with 1 inch of water, and bring to boil over high heat. Remove pan from heat, cover, and let sit for 10 minutes. Fill a medium bowl half full with cold water and add 1 tray of ice cubes. Transfer eggs to ice water bath and let sit 5 minutes.
Peel eggs and then slice the eggs in half lengthwise. Remove the yolks with a spoon, and place them in the bowl of a food processor. Set the whites aside.
Blend the yolks, mayonnaise, butter, and mustard until smooth in a food processor. Season with salt and pepper to taste. Add the chives.
Transfer the mixture to a piping bag fitted with a large star tip, or use a plastic sandwich bag with the tip of one corner snipped off.
Trim a sliver off the bottoms of the cooked egg whites before you fill them to keep them from rolling.
Pipe the yolk mixture into the egg whites and serve.