Preheat the oven to 350°F (180°C). Line 2 baking sheets with parchment paper or silicone baking mats.
In the bowl of a stand mixer fitted with the paddle attachment, lightly cream the butter on medium-high speed just until it is smooth, 1 to 2 minutes. Do not incorporate air into the butter. Scrape down the sides and bottom of the bowl.
Add the icing sugar, cornstarch, vanilla bean paste, and salt and beat on low speed, gradually increasing to medium-high speed, until the mixture is smooth and no chunks remain, 1 to 2 minutes. Scrape down the sides and bottom of the bowl. Add the flour and mini eggs and mix on low speed, gradually increasing to medium-high speed, until the flour is fully incorporated, without whipping air into the dough, 1 to 2 minutes.
Scoop twenty-one 1½-tablespoon portions of cookie dough onto each prepared baking sheet, leaving a little space between them. Gently press down on the cookies to flatten them to ¾-inch thickness. Bake, one sheet at a time, for 12 to 16 minutes, or until very lightly browned around the edges. Cool the cookies completely on the baking sheets.
You can make these cookies ahead and store them in an airtight container at room temperature for up to 2 weeks. They can be frozen, in an airtight container, for up to 2 months. Thaw them uncovered at room temperature for an hour before serving.