To make the lemon curd, whisk together juice, zest, sugar, and eggs in a 2-quart heavy saucepan. Stir in butter and cook over moderately low heat, whisking frequently, until curd is thick enough to hold marks of whisk and the first bubble appears on the surface, about 6 minutes. Transfer lemon curd to a bowl and chill, its surface covered with plastic wrap, until cold, at least 1 hour. The curd will thicken as it cools.
Buttercream
5 To make the buttercream, in a medium bowl with an electric hand mixer, beat butter until well softened around the bowl. Add powdered sugar, salt, and lemon zest and beat on low speed. Add the warm milk and whip to combine. Beat in poppy seeds. Transfer frosting to a freezer ziplock bag with the corner tip cut off or a piping bag with a medium round tip. Leave buttercream at room temperature until ready to pipe.
Assembling
6 To assemble the cookies, flip each whole egg cookie so the bottom is facing up. Pipe buttercream frosting around the edge. Spoon 2-3 teaspoons of lemon curd into the center of the cookie. Top with a cookie with a hole, press gently to sandwich and spoon a teaspoon of lemon curd into the cookie hole. Store in the refrigerator and dust with powdered sugar before serving. Cookies will last up to 3 days in the refrigerator.