In a medium mixing bowl use a hand beater or standing mixer to mix together cream cheese, butter, and coconut extract until smooth and creamy.
Beat in 2 cups of the powdered sugar. Beat in the remaining 2 cups of powdered sugar, stirring with a sturdy wooden spoon when the mixture becomes too thick to use a hand beater. A standing mixer will beat everything just fine.
Stir or beat in flaked coconut.
Cover bowl with plastic wrap and refrigerate for 30 minutes.
Line a baking sheet with parchment paper.
Use a cookie scoop or tablespoon to scoop balls of the cream cheese/coconut mixture.
Mold the ball into an egg shape and place it on a baking sheet.TIP: Dust your hands with powdered sugar or drop a ball into a bit of powdered sugar to make it easier to work with.
Continue molding eggs until mixture has all been used.
Place the baking sheet in the freezer and chill eggs for at least 1 hour.
In a microwave-safe bowl, microwave milk chocolate chips and 1 tablespoon of shortening in 30 second increments, stirring between, until chocolate is melted and smooth. Stop heating when there are still some solid pieces of chocolate and just stir until all is melted and smooth.
Remove eggs from the freezer. Using a fork, dip one egg at a time into the chocolate and flip to fully coat. Lift the egg out of the chocolate with a fork and gently tap on the side of the bowl to allow excess chocolate to drip off.
Place each dipped egg on a clean sheet of parchment paper or cooling rack.
Place dipped eggs into the refrigerator to set for about 15 minutes.
Microwave semi-sweet chocolate chips and remaining tablespoon of shortening in 30 second increments until melted and smooth.
Scoop melted chocolate into a plastic baggy or piping bag. Snip a tiny corner off of the baggy and drizzle in a zig-zag motion over chocolate coated eggs. Allow chocolate to set, about 5 minutes.
Serve immediately or keep refrigerated in an airtight container until ready to serve!