Preheat your oven to 350°F (175°C). Line your baking sheets with parchment paper.
In a large mixing bowl, beat the butter and sugar together using an electric mixer until light and fluffy, about 3-4 minutes.
Add the eggs, milk, vanilla extract, and lemon extract to the butter mixture. Beat until well combined.
In another bowl, whisk together the cake flour, all-purpose flour, baking powder, and salt. Gradually add to the wet ingredients, mixing until just combined.
Drop rounded spoonfuls of dough onto the prepared baking sheets, spacing them about 2 inches apart. Bake for 12-15 minutes or until lightly golden.
While the cookies cool, prepare the glaze by mixing powdered sugar with boiling water until smooth. Divide into two bowls and melt the bittersweet chocolate in one bowl, mixing it in.
Frost half of each cookie with the vanilla glaze and the other half with the chocolate glaze. Allow to set before serving.
