Preheat the oven to 350°F (175°C).

In a mixing bowl, cream together the softened butter and sugar until light and fluffy.

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

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

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Drop spoonfuls of dough onto a baking sheet lined with parchment paper.

Bake for 10-12 minutes or until the edges are lightly golden.

Remove from the oven and let cool completely.

In a mixing bowl, beat the softened butter until creamy.

Gradually add the powdered sugar, mixing on low speed until combined.

Add the raspberry puree and vanilla extract, mixing until smooth.

If the frosting is too thick, add milk a tablespoon at a time until desired consistency is reached.

Once the cookies are completely cooled, spread a generous amount of raspberry frosting on top of each cookie.

Serve immediately or store in an airtight container.