PREHEAT OVEN TO 350º F AND GREASE 2, 8×8-INCH BAKING DISHES WITH NON-STICK SPRAY.
WHISK WHITES IN A LARGE BOWL UNTIL FROTHY, THEN TRANSFER TO BAKING DISH.
WHISK YOLKS TOGETHER AND POUR INTO SECOND, GREASED BAKING DISH.
COVER BOTH WITH ALUMINUM FOIL AND PLACE IN OVEN. BAKE FOR 25-30 MINUTES, OR UNTIL SET.
REMOVE BOTH FROM OVEN AND TURN WHITES OUT ONTO A CUTTING BOARD. CUT INTO CUBES.
TAKE BAKED YOLKS AND TRANSFER THEM TO A FOOD PROCESSOR OR BLENDER.
PULSE UNTIL COARSE PASTE FORMS, THEN MIX IN MAYONNAISE, MUSTARD, RELISH AND HOT SAUCE, IF USING, AND SEASON WITH SALT AND PEPPER.
TRANSFER MIXTURE TO PIPING BAG (OR RESEALABLE PLASTIC BAG) AND PIPE YOLK “FILLING” ONTO EACH EGG WHITE CUBE.
TOP WITH PAPRIKA AND CHIVES AND SERVE IMMEDIATELY.