Add the melted butter, peanut butter, vanilla extract, and salt to a large mixing bowl. Beat with a hand mixer on medium until combined.
Add in the powdered sugar and beat until the powdered sugar is completely worked in.
Place the peanut butter filling between two pieces of parchment paper and roll out to about ½ inch thickness.
Slide a cookie sheet under the parchment paper and transfer the filling to the freezer. Let freeze for 1 hour.
Once frozen, quickly cut out the eggs using a 2 ½ inch egg cookie cutter. Place the eggs on a new piece of parchment paper or wax paper. Reroll any remaining filling and continue cutting out the eggs. If the filling becomes too soft to work with, pop it back in the freezer until firm.
Slide the cookie sheet under the parchment paper with the eggs on it and place them back in the freezer for 1 hour until frozen.
About 10 to 15 minutes before you remove the eggs from the freezer, add the milk chocolate chips and coconut oil to a double boiler. If you don't have a double boiler, you can place a large heat-proof bowl on top of a saucepan that has about an inch of simmering water in it. Don't let the water touch the heat-proof bowl.
Stir occasionally until the chocolate is completely melted and smooth. If your chocolate is still thick, add additional coconut oil ½ tablespoon at a time. Let it melt completely and stir in before adding more.
Remove the eggs from the freezer in small batches and dip them in the melted chocolate. Pull the eggs out of the chocolate with a fork and remove the excess chocolate by tapping the wrist that's holding the fork. Slide the bottom of the fork on the side of the heat-proof bowl to clean it off. Use a skewer to push the egg off the fork onto a piece of parchment paper or wax paper and twist the skewer as you pull it out from under the egg.
Allow the chocolate to firm up. Make it quicker by sliding the cookie sheet under the parchment paper and popping the eggs in the fridge.
Store in an airtight container in the fridge.
*The filling can be soft and will need to be frozen and worked with quickly. For a firmer filling, add an additional ¼ to ½ cup of powdered sugar.