Divide the white chocolate between 2 medium microwave-safe bowls. Add 2 teaspoons of the coconut oil to each bowl. Microwave each separately in 15-second intervals, stirring in between each, until the chocolate is melted and silky smooth. Add 1/2 teaspoon of the green food coloring to one bowl and stir to combine. Add the yellow food coloring to the other bowl along with the remaining 6 drops green food coloring and stir to combine.
Transfer the chocolate to 2 resealable plastic bags. Snip a small piece from a corner of each bag. Drizzle the dark green chocolate back and forth across the length of each cup of 2 plastic or silicone 8-cup egg molds, making sure to leave some spaces and not cover each cup entirely. Tap the molds to allow the chocolate to fall into the cups. Freeze until hard, about 10 minutes. Drizzle half of the light green chocolate back and forth across the length of the cups in each mold. Swirl and tap the molds to allow the light green chocolate to flow into the open spaces between the dark green chocolate. Freeze until hard, about 10 minutes. Drizzle the remaining light green chocolate into the cups and use your fingers or a pastry brush to distribute the chocolate throughout the cups so the insides of the eggs are entirely light green. Freeze until hard, about 10 minutes.
Meanwhile, mix the vanilla frosting with the red food coloring in a small bowl until incorporated. Tear the cake into small pieces and put in a large bowl. Fold in the frosting and mix until the cake is completely colored and can be rolled into a ball without crumbling.
Use a sharp paring knife to scrape away the scraggly edges of chocolate on the egg cups. Press 1 tablespoon of the cake mixture into each cup, smoothing out the top so it is completely flat. Press a few chocolate chips into each cake piece. Chill until ready to eat, 4 hours and up to overnight.
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