Preheat the oven to 325°F (165°C). Line an 8x8-inch baking dish with parchment paper, leaving overhang on the sides for easy removal.
In a large mixing bowl, beat the butter with a hand mixer until light and fluffy. Mix in the vanilla extract and powdered sugar until smooth. Add the egg and mix until combined.
Gradually add the flour and kosher salt, mixing just until a dough forms. Set aside.
In a medium bowl, stir together the brown sugar, cinnamon, flour, melted butter, and vanilla extract until fully combined.
Divide the dough in half. Press half evenly into the bottom of the prepared baking dish. Spread the cinnamon filling evenly over the dough layer.
Top with the remaining dough, pressing gently to cover the filling. If needed, lightly oil your hands or use parchment paper to help spread the dough evenly.
Bake for 40 minutes, or until the bars are set and the edges are lightly golden. A toothpick inserted into the center should come out clean or with a few crumbs.
Let the bars cool in the pan on a wire rack for about 40 minutes. While the bars cool, prepare the icing by stirring together the powdered sugar, cinnamon, and vanilla extract until smooth and spreadable.
Spread the icing evenly over the cooled bars and let it set for about 15 minutes. Lift the bars from the pan using the parchment overhang. Slice into 8 bars and serve.