
Place butter in a large mixing bowl and use an electric mixer to beat until smooth and creamy.
Add powdered sugar and mix until sugar is completely absorbed and mixture is smooth.
Add vanilla extract and stir to combine.
In a separate, medium-sized mixing bowl, whisk together flour, cornstarch, and salt until combined.
Gradually add the flour mixture to the butter mixture, stirring on low-speed until completely combined.
Form dough into a disk, wrap in plastic wrap, and place in the refrigerator to chill for at least 60 minutes (see note).
When the cookie dough is finished chilling and you are ready to bake, preheat your oven to 350F (175C) and line a baking sheet with parchment paper. Set aside.
Remove dough from the refrigerator and place on a clean, lightly floured surface. Use a rolling pin to roll dough out to ⅛”-¼” (about 0.5 cm) thickness. Use your egg-shaped cookie cutter to cut out as many cookies as possible. Gather any remaining scraps into a ball and re-roll to make more cookies.
Using your circle cookie cutter, make a circular cut into half of the egg cookies (I like to make the circle cut centered in the lower half of the egg). You can reroll the circle pieces you’ve rolled out.
Transfer cookies to prepared baking sheet, spacing cookies at least 2” apart (it is best to bake the cookies without cutouts on one pan, and the cookies with cutouts on a separate pan so that they will all bake evenly).
Bake in center rack of preheated 350F (175C) oven for 8-10 minutes, until the edges of the cookies are just beginning to turn a light golden brown. Allow cookies to cool completely before assembling.
Once cookies are cooled, dust all of the eggs with cutouts only with powdered sugar (I place the cookies on a piece of wax paper for easy cleanup, then use a small sifter to sift sugar all over these cookies).
Take a whole egg cookie and flip it over so the bottom is facing up. Dollop a teaspoon of lemon curd into the center.
Take a sugared cookie and gently but firmly settle over the lemon curd, lining up the edges of the cookies and gently pressing so they stick together. Repeat with all cookies.