Preheat the oven to 350°F (175°C) and line two large baking sheets with parchment paper.
In a stand mixer, cream together the softened butter, 3/4 cup brown sugar, and granulated sugar for 3 minutes until light and fluffy.
Add the egg and vanilla extract, beating until fully incorporated.
In a medium bowl, whisk together the flour, baking soda, salt, and 1 teaspoon of ground cinnamon.
Gradually incorporate the dry ingredients into the butter mixture on low speed until a soft dough forms.
Prepare the filling by mixing the remaining 1/2 cup brown sugar, 1 teaspoon of cinnamon, and 1 tablespoon of melted butter in a small bowl until the texture resembles wet sand.
Scoop approximately 2 tablespoons of dough, flatten it into a disc, place 1 teaspoon of the filling in the center, and fold the edges over to seal the filling completely.
Roll the filled dough into a ball and place on the prepared baking sheets, spaced 2 inches apart.
Bake for 10 to 12 minutes, or until the edges are golden but the centers remain soft.
Cool the cookies on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Whisk together the powdered sugar, milk, and maple extract until smooth. Drizzle the glaze over the cooled cookies and allow it to set before serving.