Preheat oven to 350°F. Line 2 large cookie sheets with parchment paper or silicon baking mats. Set aside.
In a standing mixer, cream the butter and sugar until light and fluffy, about 2 minutes. Add in egg and beat on medium speed until combined. Add in lemon extract, vanilla extract, baking powder, salt, and poppy seeds and beat until combined. Remove from mixer and fold in flour and cornmeal.
Roll tablespoons of dough into balls and place on cookie sheets at least 1.5″ apart. You should have at least 40 dough balls total. Use the back of a cup or flat surface to push the ball into a circular disk (you may have to dust with flour to keep it from sticking to the dough balls). Bake for 8 minutes, then remove immediately from oven and allow to cool on a cooling rack.
While the cookies are cooling, make the frosting. Beat the butter until light and fluffy, then add the salt, lemon juice, lemon zest, and lemon extract, beating until combined. Slowly add the powdered sugar and beat for an additional minute.
Place frosting into a piping bag fitted with a small star tip. If you’d like, you can place a small stripe of yellow gel food coloring in the bag for a pop of color. Frost 1/2 the cookies, then sandwich them together with the remaining 1/2 of cookies. Devour.