Add the butter, granulated sugar, and brown sugar to a bowl. Beat on medium-high speed for 2-3 minutes. Add the vanilla and eggs and beat for another 1-2 minutes, until light and fluffy.

Whisk the dry ingredients (cake flour, cornstarch, baking soda, baking powder, kosher salt) in a separate medium bowl until combined. Add the dry ingredients to the wet ingredients and beat on medium speed until combined, about 1-2 minutes, stopping to scrape down the bowl as needed. Cover and chill the dough for one hour.

Preheat the oven to 350?F and line two large baking sheets with parchment paper.

Add the filling ingredients (butter, brown sugar, cinnamon, cake flour) to a medium bowl and stir until smooth. Use a heaping teaspoon to scoop the filling out and roll it into a ball, placing it on the baking sheet.

Scoop the chilled dough using a 1/4 cup measuring cup. Break the dough in half and create a well in the middle of one half. Place one ball of filling inside the well and press the other half on top. Pinch the seams and roll into a ball to seal the filling inside.

Arrange the cookie dough balls on the prepared baking sheet about 2 inches apart. Bake for 11-13 minutes, until the tops are just set and the edges are lightly golden brown. Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.

While cooling, make the icing by whisking together all icing ingredients until smooth. Place parchment paper under the cooling rack and spoon icing on top of each cookie, allowing it to spread. Let set for 15 minutes and enjoy.