Prepare Egg Shells:
Use a push pin to pierce the wider bottom end of the egg. Poke a few times to hollow out about 1/4 inch hole. Use a wooden skewer to to stir and break up the yolks inside the shells. Using a strainer (to make sure no shells spill out) and over a bowl, give the egg a good shake over the strainer over the bowl to get all the egg out of the shells. Set aside.
Rinse out each egg shell. Set in a large pot of salt water for 1 hour.
Rinse the eggs out thoroughly and shake out any extra water. Flip upside down on a towel and towel dry outside shell.
Drizzle coconut oil inside and outside of shell. Cover the opening hole with finger and shake around to coat interior with the oil. Shake the extra oil out by rolling the egg in the air over a towel in a circular motion with the hole on the bottom.
Crumble 3 cupcake liners around the narrow end (closed end) of each eggshell and set the shells hole side up in the cups of a cupcake pan.
Pour batter into a pastry bag or Ziplock bag. If using a Ziplock bag, cut 1/8 of one corner. Fill each egg with about 3 Tablespoons or 3/4 full of batter.
Preheat oven 350 Degrees F.
In a mixing bowl, combine 1 cup of eggs, 1/4 cup coconut oil, apple sauce, vanilla, coconut milk, Xylitol (or sugar). Mix on medium speed until blended.
In a small bowl combine flour and baking powder. Add to wet mixture. Continue on low speed for 1 minute.
Use a pastry bag with a 1/16-inch plain tip to fill each egg with about 3 tablespoons of batter or 3/4 full. Or if making without egg, fill cupcake lined muffin tins each 1/2 full.
Bake 25-30 minutes, or until a wooden skewer inserted into the center of the eggs or cupcakes comes out clean. Let set 10 minutes then remove from the muffin pan and transfer to a cooling rack to cool completely. Use a damp towel to wipe off any spatters or overflowing batter from the egg.
Store in an airtight container.