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 until smooth in a food processor. Season with salt and pepper to taste.
Trim a sliver off the bottoms of the cooked egg whites before you fill them to keep them from rolling.
Dip the cut surfaces of the eggs into the cocoa powder or squid ink. Set aside.
Stir the gochujang and if you want the color more orange, stir in paprika, to taste.
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. Pipe the yolk mixture into the egg whites. Punch shapes using craft punches and place on top of the egg yolk along with roe, if using.