In a large bowl, beat together the peanut butter and softened butter until smooth and well combined.
Add the vanilla extract and salt. Mix until incorporated.
Gradually add the powdered sugar, about half a cup at a time, mixing well after each addition until a thick dough forms.
Line a baking sheet with parchment paper. Scoop about two tablespoons of filling at a time, roll between your palms, and shape into an egg. Place on the prepared baking sheet. Repeat with remaining filling.
Freeze the shaped eggs for 20 to 30 minutes until very firm.
In a microwave-safe bowl, combine the chocolate chips and coconut oil. Microwave in 30-second intervals, stirring after each, until completely melted and smooth.
Using a fork, dip each chilled egg into the melted chocolate, turning to coat completely. Tap the fork gently on the edge of the bowl to remove excess chocolate. Return to the parchment-lined baking sheet.
Drizzle any remaining melted chocolate over the tops of the eggs using a fork for decoration.
Sprinkle with flaky sea salt if desired while the chocolate is still wet.
Refrigerate for at least 30 minutes or until the chocolate coating is completely set. Serve chilled.