Add the butter, granulated sugar, and brown sugar to the bowl of a stand mixer or hand mixer fitted with the paddle attachment. Beat on medium-high speed for 2–3 minutes until light and fluffy. Add in the eggs and vanilla extract and beat again for another minute or two.
In a separate medium bowl, whisk together all dry ingredients until well combined. This includes cake flour, cornstarch, baking soda, baking powder, and kosher salt.
Gradually add the dry mixture into your wet ingredients and mix on medium speed until just combined—about 1–2 minutes. Cover your dough with plastic wrap and chill it in the fridge for one hour.
Preheat your oven to 350°F (175°C). In a medium bowl, combine softened butter, light brown sugar, cinnamon, and cake flour until smooth. Roll into small balls and set aside.
Once chilled, use a measuring cup or large cookie scoop to portion out roughly one-fourth of your dough. Create a well in one half and place one filling ball inside. Press down gently with the other half of dough on top and pinch seams together to seal.
Arrange your formed cookie balls on prepared baking sheets about two inches apart. Bake for about 11–13 minutes until tops are set with lightly golden edges. Allow to cool on the baking sheet for five minutes before transferring to a wire rack.
Whisk together all glaze ingredients until smooth. Spoon icing over each cookie generously so it spreads toward the edges beautifully. Allow to set for around fifteen minutes before serving.