Cut each egg in half lengthwise. Transfer hard-boiled egg yolks to a mixing bowl. Melt
butter in a saute pan, and gently cook apples and shallots
until tender. Remove from heat and add parsley to apple mixture and let cool. Mix yolks with mayonnaise
and mustard, and season with salt and pepper, to taste. Spoon apple mixture into empty hard boiled egg whites. Spoon egg mixture on top of apple. Garnish
with lemon-thyme or fresh mint.