In a small bowl, whisk together the light brown sugar, ground cinnamon, and all-purpose flour until evenly combined. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment, beat the unsalted butter, light brown sugar, and dark brown sugar on medium speed until light and fluffy, about 3-4 minutes. The mixture should be pale in color.

In a separate bowl, whisk together the cake flour, all-purpose flour, cornstarch, baking soda, and kosher salt. Gradually add this dry mixture to the butter-sugar mixture, mixing on low speed just until combined. Do not overmix.

Mix in the eggs and vanilla extract until fully incorporated.

Scoop about 1 1/2 tablespoons of dough (using a cookie scoop for uniformity) and flatten it slightly in your palm. Place about 1/2 teaspoon of the cinnamon filling in the center. Carefully fold the edges of the dough over the filling to seal it completely, rolling into a ball. Repeat with the remaining dough and filling.

Place the stuffed dough balls on a plate or tray and refrigerate for at least 30 minutes to prevent spreading during baking.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper. Arrange chilled dough balls on the baking sheets, spacing them about 2 inches apart. Bake for 10-12 minutes, until the edges are just barely golden. The centers may still look slightly underdone, but they will set as they cool. Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

In a small bowl, whisk together the powdered sugar, milk, and maple syrup until smooth and thick but pourable. If too thick, add more milk by the teaspoon. Drizzle the icing over the cooled cookies and sprinkle with a pinch of ground cinnamon for extra flavor.