Peel hard-boiled eggs and slice in half lengthwise. Remove yolks and push through a fine mesh sieve or mash until very smooth.
Mix in mayonnaise, a little soft butter (this was the contest secret), a dash of yellow mustard, and a splash of vinegar. Season with salt and pepper. Pipe or spoon the creamy yolk mixture back into egg white halves. Sprinkle with paprika. Chill until serving.