Method

• 01
  Place egg on a cutting board on its side. Make two cuts, one very thin one at the bottom so the egg will sit flat and another 3/4 of the way up, taking off the top like a lid. Repeat with all 12 eggs.
• 02
  Carefully remove yolks and place them in a separate bowl. You might need to use a potato nail or toothpick to get out all of the yolk. Mash or grate until it is fine bits.
• 03
  In a large mixing bowl with an electric mixer or the bowl of a stand mixer fitted with the paddle attachment, blend egg yolks with dijon mustard, hot sauce, and white vinegar to form a paste.
• 04
  Add mayonnaise, fine sea salt, and white pepper, beating until smooth.
• 05
  Transfer mixture to a piping bag or plastic seal bags with the corner snipped. Fill each egg generously up and beyond the brim. Top with the "lid." Continue with remaining eggs.
• 06
  Cut olives into small, square pieces using kitchen shears. Using a vegetable peeler, shave off small pieces of carrot, trimming with kitchen shears to get the desired shape. Use olive pieces for eyes and carrot shavings for the nose. It is easiest to place these using tweezers.