Preheat oven to 350°F (175°C) and line a 9x9-inch baking pan with parchment paper.
In a large bowl, whisk together flour, sugar, brown sugar, baking powder, baking soda, and salt.
Stir in melted butter, milk, vanilla extract, and egg until combined into a smooth batter.
In a small bowl, mix brown sugar, cinnamon, and softened butter for the swirl.
Pour half of the batter into the prepared pan and spread evenly.
Sprinkle the cinnamon swirl mixture over the batter.
Pour the remaining batter on top and gently spread to cover.
Bake for 25 minutes or until a toothpick comes out clean.
Let cool completely in the pan.
Mix powdered sugar, milk, and vanilla to make glaze and drizzle over cooled bars.
Cut into squares and serve.