Preheat the oven to 350°F (175°C).

In a large bowl, cream together 1 cup of unsalted butter, 1/2 cup granulated sugar, and 1 cup packed light brown sugar until smooth.

Beat in the 2 large eggs and 1 teaspoon vanilla extract until well combined.

In a separate bowl, whisk together 3 3/4 cups cake flour, 2 tablespoons cornstarch, 1 teaspoon baking soda, 1 1/2 teaspoons baking powder, and 1 teaspoon kosher salt.

Gradually add the dry ingredients to the wet mixture and mix until just combined.

On a floured surface, roll out the cookie dough and cut it into desired shapes.

In another bowl, combine 5 tablespoons softened unsalted butter, 3/4 cup packed light brown sugar, 1 teaspoon cinnamon, and 2 tablespoons cake flour until smooth.

Fill half of the cookie shapes with the cinnamon filling and top with the remaining cookie shapes.

Bake in the preheated oven for 10 minutes or until golden brown.

Allow cookies to cool before icing.

For the icing, whisk together 1 cup powdered sugar, 1/2 teaspoon cinnamon, 3 tablespoons melted and cooled unsalted butter, and 2 1/2 tablespoons milk until smooth.

Drizzle icing over cooled cookies.