In the bowl of a stand mixer fitted with the paddle attachment cream together butter and sugar until light in color, about 4 minutes.
Add the egg and milk and beat until combined.
Sift together flour, baking powder, and salt.
Gradually add the flour mixture with the mixer running on low speed. Beat until the dough pulls away from the side of the bowl.
Divide the dough in half and wrap in plastic wrap. Refrigerate for 2 hours.
Preheat oven to 375°F and prepare a cookie sheet with parchment paper or a silicone baking mat.
Sprinkle surface with powdered sugar and roll out one pack of dough at a time to 1/4-inch thick (leave the other pack of dough in the fridge).
Use an egg-shaped or circle cookie cutter (2.5-3-inches diameter)and cut the dough into shapes. Place the shapes at least 1-inch apart on the prepared baking sheet. Then use a small circle cutter or measuring spoon and punch a hole in the middle of half the cookies.
Bake for 7-9 minutes or until cookies are just starting to brown around the edges. Rotate the cookie sheet halfway through baking time.
Let the cookies cool on the baking sheet for 3 minutes then transfer to a wire rack to cool completely.
When the cookies are completely cooled, make the icing. Mix powdered sugar with lemon juice until you have a quite thick mixture. You'll only ice the cookies with the holes. Start with the border icing, let it dry for 1-2 minutes and then fill in the interior of the cookie. Let them dry.
Spread lemon curd on the bottom cookies then press a top cookie carefully on top. Fill the hole with more lemon curd.
Store the dried cookies in an airtight container stacked between sheets of parchment paper in a cool place.