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

In a medium bowl, whisk together flour, baking powder, baking soda, and salt.

In a large mixing bowl, cream butter, granulated sugar, and brown sugar until light and fluffy.

Beat in eggs one at a time, then mix in sour cream, milk, lemon zest, lemon juice, and vanilla extract.

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

Drop rounded tablespoons of batter onto prepared baking sheets, spacing 2 inches apart.

Bake for 10–12 minutes, until edges are set and tops spring back when touched. Let cool completely.

Meanwhile, prepare the filling: beat butter and cream cheese until smooth. Add powdered sugar, lemon juice, and lemon zest, and beat until fluffy.

Spread or pipe filling onto the flat side of half the cookies, then top with the remaining cookies to make sandwiches.

Refrigerate for 30 minutes before serving for best texture.