Prep the pans: Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper.
Whisk dry ingredients: In a bowl, whisk flour, baking soda, baking powder, salt, and cinnamon.
Set aside.
Cream the butter and sugars: In a large bowl, beat softened butter with brown sugar and granulated sugar until light and fluffy, 2–3 minutes.
Add eggs and vanilla: Beat in the egg, egg yolk, and vanilla until smooth.
Combine: Add dry ingredients to the wet and mix on low just until the dough comes together. Do not overmix.
Make the filling: Stir brown sugar, cinnamon, melted butter, and a pinch of salt until it looks like damp sand.
Shape the cookies: Scoop dough into 2-tablespoon balls. Flatten each slightly, add 1 teaspoon of filling to the center, and fold the edges over to seal.
Place seam-side down on the baking sheet, spacing 2 inches apart.
Bake: Bake 10–12 minutes, until edges are set and centers look slightly underdone. They’ll finish setting as they cool.
Cool: Let cookies rest on the sheet for 5 minutes, then transfer to a rack to cool completely.
Make the icing: Whisk powdered sugar, brown sugar, vanilla, and 1 tablespoon milk. Add more milk, a few drops at a time, until thick but spoonable.
Stir in a pinch of cinnamon if you like.
Glaze: Spoon icing over cooled cookies, letting it slowly spread. Allow 20–30 minutes for the icing to set.