In a large mixing bowl, combine the all-purpose flour, brown sugar, and salt. Using an electric mixer or your hands, blend in the softened butter until the mixture resembles coarse crumbs. Add the egg, milk, and vanilla extract, then mix until a smooth dough forms. Avoid overmixing to keep the texture tender.
Lightly flour your work surface and roll out half of the dough into a rectangle about 8x8 inches. Place this dough layer into the bottom of your greased baking pan, pressing gently to cover the entire base evenly.
In a small saucepan, combine the granulated sugar, light corn syrup, water, and ground cinnamon. Heat over medium heat, stirring constantly until the sugar dissolves and the mixture thickens slightly, about 3-4 minutes. Remove from heat and let cool for a few minutes so it’s warm but not hot.
Pour the cinnamon filling evenly over the dough layer in the pan. Then, roll out the remaining dough to the same size and carefully place it on top of the filling layer, sealing the edges by gently pressing with your fingers or a fork to prevent leaking.
Preheat your oven to 350°F (175°C). Bake the bars for 25-30 minutes or until the top is golden brown and the filling bubbles slightly around the edges. Remove from the oven and allow to cool completely on a cooling rack.
In a small bowl, whisk together the icing sugar and 1 tablespoon of milk. Add more milk, a little at a time, until you achieve a smooth, drizzle-able consistency. Drizzle the frosting over the cooled pastry bars. Let the frosting set before slicing into bars.