Cream corn syrup and butter together using a stand mixer or hand mixer. Slowly add icing sugar with mixer on low speed and mix until fully combined. Add vanilla.
Transfer about 1/3 of the mixture into a small bowl and add yellow food coloring to make the yolks. Allow both white and yellow fillings to chill in the fridge for 15-20 minutes.
Remove yellow filling from fridge. Pull off small pieces (about 1 tsp) and roll into balls. Place on a tray lined with wax paper and put them back in the fridge.
Remove white filling from fridge. Pull off larger pieces (about 1 Tbsp) and flatten into round patties. Place a yellow ball in the center of each patty and wrap the patty around the yellow ball. Form each piece of filling into an egg shape, re-chilling if it becomes to soft and sticky to work with. Place the tray of egg shapes into the fridge to re-harden.
For the chocolate coating
Melt chocolate and coconut oil using a double boiler or glass bowl set over a pot of gently simmering water. Dip each egg shape into the melted chocolate using a spoon or fork. Shake off excess chocolate and set on a tray lined with wax paper. Allow the chocolate to set in fridge of freezer. If you have any additional melted chocolate left after coating all eggs, feel free to re-dip some or all of the eggs for a thicker chocolate shell, if you wish.