Preheat the oven to 275 degrees F (135 degrees C). Line a baking sheet with parchment paper.
Place chocolate eggs into a resealable plastic bag; seal the bag. Mash chocolate eggs with a heavy measuring cup a few times. You don't want them pulverized, just cracked into small-to-medium-sized pieces.
Combine flour, cornstarch, sugar, and salt in a large bowl. Add butter. Beat using an electric mixer until you get a workable dough. Add the crushed chocolate eggs and mix until well combined.
Roll dough into ping pong-sized balls. Flatten balls slightly and lay onto the prepared baking sheet.
Bake in the preheated oven until the very edges of the cookies start to brown, about 22 minutes.