Carefully poke a small hole in the top of each egg. I found that the easiest way to do this was to use the tip of a corkscrew bottle opener.
Once you have poked tiny holes in your eggs, peel back the edges of the holes to expand them a bit. The holes will need to be large enough to fit the tip of a piping bag inside. You can always make the holes larger when you are ready to pipe, so err on the smaller side during this step.
Turn the egg upside down and dump out the contents. I used the tip of a thermometer to help get all of the egg out of the shell. Keep the contents of one egg separate to use in the cake recipe. If you plan on using the other eggs for baking, it might be helpful to store them in small plastic containers in groups of two (otherwise it will be hard for you to later tell how much of your big bowl is two eggs).
Rinse the insides of the eggs out thoroughly over a sink. Then, roll them around and immerse them in saltwater for thirty minutes. They will have to be filled with the saltwater in order to sink completely.
Rinse the eggshells in cold water and lay the eggs hole side down on a paper towel to drain and dry.
Cake Instructions
Mix flour, baking powder, baking soda, and salt in a medium-sized bowl and set aside.
In a large bowl, mix one egg and sugar until light and creamy.
Add the butter and lemon extract and mix until fully integrated.
Mix in the dry ingredients until just combined.
Add the sour cream and mix until smooth.
Place the prepared eggshells into a muffin tin. Use aluminum foil in each well to help them stand upright.
Load the batter into a piping bag fitted with a large round tip. Make sure that the tip can fit all of the way inside of the hole in each egg. If it can't, slowly expand the hole a little bit at a time until it fits.
Fill each egg about 3/4 full with batter. If you underfill the eggs, you won't have a complete cake egg inside when you crack them after baking. If you overfill the eggs, cake will overflow out of the eggs during baking.
Bake the eggs at 350 F for 23 minutes.
Let cool, crack, and eat!
Video
Notes
If cupcakes have overflown or look messy right after baking, remove excess cake and clean the eggshells with a damp towel. I found that it was best to let the cake overflow out of the top of the eggs and then simply pick it off (eat it) and clean the shell with a damp towel before serving.