1 Make the brown sugar filling. In a small bowl, stir together the brown sugar, melted butter, cinnamon, flour, and salt until a thick paste forms.
2 Portion the filling. Divide the filling into 10 small portions, about 1½ teaspoons each. Place them on a parchment-lined plate and gently flatten each portion into a small disc. Freeze for 20–30 minutes, or until firm.
3 Make the cookie dough. Add the softened butter, brown sugar, and granulated sugar to a large mixing bowl. Beat with an electric mixer for 2–3 minutes, until light and creamy.
4 Add the egg, egg yolk, and vanilla. Beat until smooth and fully combined, scraping down the sides of the bowl as needed.
5 Combine the dry ingredients. In a separate bowl, whisk together the cake flour, all-purpose flour, cornstarch, baking soda, baking powder, salt, and cinnamon.
6 Finish the dough. Gradually add the dry ingredients to the wet ingredients. Mix on low speed just until a soft dough forms. Do not overmix.
7 Chill the dough. Cover and refrigerate for 20–30 minutes, or until the dough is firm enough to easily shape around the filling.
8 Preheat the oven. Preheat the oven to 350°F and line two baking sheets with parchment paper.
9 Stuff the cookies. Scoop about 3 tablespoons of cookie dough and flatten it into a thick disc. Place one frozen cinnamon brown sugar filling disc in the center. Bring the edges of the dough up and around the filling, completely sealing it inside. Gently roll into a ball.
10 Bake. Arrange the cookies about 3 inches apart on the prepared baking sheets. Bake for 11–13 minutes, or until the edges are set and the centers still look slightly soft and underbaked.
11 Cool. Let the cookies cool on the baking sheet for about 10 minutes, then transfer them to a wire rack to cool completely before glazing.
12 Make the cinnamon glaze. Whisk together the powdered sugar, melted butter, vanilla, cinnamon, salt, and 1½ tablespoons of milk. Add additional milk, a small amount at a time, until the glaze is thick but spreadable.
13 Glaze the cookies. Spoon the glaze onto the center of each cooled cookie and gently spread it toward the edges. Allow the glaze to set for 20–30 minutes before serving.
