In a large bowl, whisk together the flour, cornstarch, baking powder, and salt. Set aside.

In the bowl of a stand mixer fitted with a paddle attachment, cream together the butter and sugar. Add the eggs, one at a time until fully combined.

Mix in half of the flour mixture. Stir in half of the milk. Add the remaining flour mixture and stir just until combined. Finish with the remaining milk, lemon juice, lemon zest, and vanilla. Mix until combined.

Using a small cookie scoop (mine was about 1 1/2" in diameter) or two small spoons, scoop batter onto the prepared baking sheet, leaving 2 inches between cookies. Bake for 10-12 minutes, or until tops are springy. Cool on the pan for 2 minutes before transferring to a wire rack to cool completely.

Using a stand mixer or a hand mixer and a large bowl, cream the butter and jam together. Add the milk and lemon juice and continue mixing until combined.

Gradually add the powdered sugar, a cup at a time, mixing after each addition until all 4 cups have been added. Mix for an additional 2 minutes on high until light and fluffy.

Pair each cookie with a cookie that matches its shape and size. Using a pastry bag fitted with a large star tip*, pipe about 2 tablespoons of buttercream onto one cookie. Top with another cookie.