Preheat your oven to 350°F. Line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and ground cinnamon. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy, about 2-3 minutes. Add the egg and vanilla extract, mixing until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
In a small bowl, combine the brown sugar and 1 tablespoon of ground cinnamon to create the filling.
Take a portion of the cookie dough (about 2 tablespoons) and flatten it into a disk. Sprinkle a teaspoon of the cinnamon filling in the center, then fold the edges over to seal. Roll the dough into a ball and place it on the prepared baking sheet. Repeat with the remaining dough and filling, spacing the cookies about 2 inches apart.
Bake for 10-12 minutes, or until the edges are lightly golden. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
In a small bowl, whisk together the powdered sugar, milk, and ½ teaspoon of vanilla extract until smooth. Drizzle the icing over the cooled cookies.