Add the butter, granulated sugar, and light brown sugar to the bowl of a stand mixer, or to a hand mixer fitted with the paddle attachment. Beat on medium-high speed for 2-3 minutes. Then, add the vanilla extract and eggs, and beat for an additional 1-2 minutes, until the mixture becomes light and fluffy.
1 cup unsalted butter, ½ cup granulated sugar, 1 cup light brown sugar, 2 eggs, 1 teaspoon vanilla extract
In a separate medium bowl, whisk together the dry ingredients until well combined. Gradually add the dry ingredients to the wet ingredients and beat on medium speed for 1-2 minutes, until fully incorporated. Make sure to stop and scrape down the sides and bottom of the bowl as needed. Cover the dough and refrigerate for one hour.
3 ¾ cups cake flour, 2 tablespoons cornstarch, 1 teaspoon baking soda, 1 ½ teaspoons baking powder, 1 teaspoon kosher salt
Preheat the oven to 350°F and line two large baking sheets with parchment paper.
In a medium bowl, combine the filling ingredients and stir until smooth. Using a heaping teaspoon (about 2 teaspoons), scoop the filling and roll it into a ball, then place it on the prepared baking sheet.
5 tablespoons unsalted butter, ¾ cup light brown sugar, 1 teaspoon cinnamon, 2 tablespoons cake flour
Scoop out the chilled dough using a ¼ cup measuring cup (or a large cookie scoop). Divide the dough in half and create a well in the center of one half. Place one ball of filling into the well, then press the other half of dough on top, sealing the filling inside. Pinch the seams together and roll the dough into a ball.
Arrange the cookie dough balls on the prepared baking sheet, spacing them about 2 inches apart. Bake for 11-13 minutes, or until the tops are just set and the edges are lightly golden brown. Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.
While the cookies cool, prepare the icing. In a bowl, whisk together all of the icing ingredients until smooth. Place a piece of parchment paper under the cooling rack and spoon the icing over each cookie, allowing it to spread to the edges. Let the icing set for about 15 minutes before enjoying.