Cream the butter and sugars: Combine the butter, powdered sugar, cane sugar and lemon extract in a large mixing bowl (or the bowl of your stand mixer). Using a flat beater (or paddle attachment) to cream the mixture until no chunks of butter remain and the mixture looks smooth.

Make the cookie dough: Add in the milk and sourdough starter until well combined. The acidity in the starter may cause your mixture  to appear separated and curdled, this is totally normal. Fold the flour, baking powder, salt and lemon zest. Mix on low until no bits of dry flour remain.

Chill the dough: Refrigerate the dough for 15 to 20 minutes or until the dough is not too sticky.

Portion out the dough: Using a cookie scoop, divide the dough into 24 portions and place them on the prepared baking sheet, about 1-inch apart to allow them to spread.

Bake: Bake the cookies for 11 to 14 minutes or until the tops of the cookies look cracked and dry, and the edges look set.

Make the filling: Add powdered sugar, butter and lemon juice to a large mixing bowl. Mix on low until combined and then speed up the mixer until the mixture is light and fluffy, about 1 minute. Transfer the filling to a piping bag fitted with an Ateco tip #864. (If you don’t have a piping bag, you can use an offset spatula.)

Allow cookies to cool completely: Transfer the cookies to a wire rack and pair them up according to size. Let the cookies cool before filling them or your buttercream will melt.

Assemble sandwich cookies: Pipe the filling on half of the cookies and sandwich them together.

Store: Store the cookies in an airtight container in the refrigerator for up to 3 days.