In a large bowl, use an electric mixer to cream room temperature butter until light and fluffy. Add vanilla and condensed milk; beat until blended.
Add powdered sugar, 2 cups at a time, blending well after each addition.
Transfer mixture to parchment paper; knead to a smooth fondant consistency.
Use a small cookie scoop (about 1 T.) per egg; roll between hands and pinch at one end to form a smooth egg shape.
Place eggs on rimmed cookie sheet lined with parchment paper. Refrigerate for 2-3 hours.
When ready to coat, melt chocolate at 50% power in microwave in 30 second intervals until mostly melted; stir to smooth. Slightly cool before next step.
Drop firmed buttercream eggs into chocolate, one at a time. Use a fork to roll and coat the eggs (but do not puncture eggs with fork).
Use the fork to gently lift the eggs out of the chocolate (without piercing them) and onto a rimmed cookie sheet lined with new parchment paper.
Decorate immediately if desired; then refrigerate eggs for 1 more hour to set.
Store eggs in an airtight container and keep refrigerated. Use parchment paper in between layers so the eggs don't stick together. Enjoy within 5-7 days.