For the Lemon Filling:

1. In a medium saucepan, whisk together lemon juice, lemon zest, sugar, and cornstarch until smooth.
2. Add the egg yolks and whisk until combined.
3. Heat the mixture over medium heat, whisking constantly, until it thickens, about 5–7 minutes.
4. Remove from heat and stir in butter until melted and smooth.
5. Transfer the filling to a bowl, cover with plastic wrap (press it directly onto the surface to prevent a skin from forming), and refrigerate until cool and thickened.

For the Cookies:

1. Prepare the dough:
   In a large mixing bowl, cream the butter and sugar together until light and fluffy. Add the egg, vanilla extract, and lemon zest, mixing until well combined.
2. Mix the dry ingredients:
   In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, mixing until a dough forms.
3. Chill the dough:
   Divide the dough into two discs, wrap in plastic wrap, and chill in the refrigerator for 30 minutes.
4. Roll and cut the cookies:
   Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper. Roll out the chilled dough on a lightly floured surface to about ¼-inch thickness. Use a round cookie cutter (or any shape you prefer) to cut out cookies. For half the cookies, cut a small hole in the center to create “tops” for sandwiching.
5. Bake:
   Arrange the cookies on the prepared baking sheets, spacing them slightly apart. Bake for 10–12 minutes or until the edges are lightly golden. Let the cookies cool completely on a wire rack.

Assemble the Cookies:

1. Once the cookies have cooled, spread about 1 teaspoon of the cooled lemon filling onto the bottom side of a cookie.
2. Top with a “cut-out” cookie to create a sandwich. Repeat with the remaining cookies and filling.
3. Dust with powdered sugar for a decorative touch if desired.