Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the vanilla extract.
Gradually add the flour and mix until just combined. Press about two-thirds of the dough into the prepared baking pan to form the base.
In a separate small bowl, combine the brown sugar and cinnamon. Stir in the melted butter until well combined.
Spread the cinnamon sugar mixture evenly over the shortbread base.
Crumble the remaining shortbread dough over the cinnamon filling.
Bake for 25-30 minutes, or until the edges are golden brown and the filling is bubbly.
Let the bars cool in the pan for about 15-20 minutes before cutting. If making the glaze, whisk together powdered sugar, milk, and vanilla extract until smooth. Drizzle over the warm bars.
Cut into bars and serve warm or at room temperature.
Notes
These cinnamon roll bars are best enjoyed fresh, but can be stored in an airtight container at room temperature for up to 3 days.