Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a large bowl, cream together 1 cup of butter and granulated sugar until light and fluffy.

Add the egg, lemon zest, and lemon juice, beating until well combined.

In a separate bowl, whisk together the flour, baking powder, and salt.

Gradually incorporate the dry ingredients into the wet mixture until a cohesive dough forms.

Roll the dough into 24 uniform balls and place them on the baking sheets, flattening slightly with the palm of your hand.

Bake for 10 to 12 minutes until the edges are just set but not browned.

Transfer cookies to a wire rack and allow to cool completely.

For the frosting, beat the remaining 0.5 cup of butter with powdered sugar, strawberry puree, and vanilla extract until smooth and stiff.

Pipe or spread the strawberry frosting onto the flat side of 12 cookies.

Top each with the remaining 12 cookies to create sandwiches, pressing gently to adhere.