**Preheat the Oven:** Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper or a silicone baking mat.

**Cream Butter and Sugar:** In a large mixing bowl, beat the softened butter and granulated sugar together until light and fluffy, about 2-3 minutes.

**Add Wet Ingredients:** Mix in the egg, lemon juice, lemon zest, and vanilla extract until well combined.

**Combine Dry Ingredients:** In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Gradually add the dry ingredients to the wet mixture, stirring until a soft dough forms.

**Scoop and Shape:** Use a cookie scoop or tablespoon to portion out dough, rolling each piece into a ball. Place the balls on the prepared baking sheet, spacing them about 2 inches apart.

**Bake:** Bake the cookies for 8-10 minutes, or until the edges are set and the centers look slightly underbaked. Allow the cookies to cool on the baking sheet for 2-3 minutes before transferring to a cooling rack.

**Make the Lemon Cream Filling:** In a medium bowl, beat the softened butter, powdered sugar, lemon juice, and lemon zest until smooth and creamy. Adjust the consistency with more powdered sugar or lemon juice as needed.

**Assemble the Cookies:** Spread a generous amount of lemon cream filling on the flat side of one cookie and sandwich it with another cookie. Repeat with the remaining cookies.