Preheat the oven to 325℉, then grease and line an 8x8 square baking pan with parchment paper and set aside.
To a medium bowl, add all of the filling ingredients—the brown sugar, cinnamon, flour, melted butter, and salt. Stir until a sandy mixture forms, then set aside.
In a large bowl with a hand mixer or stand mixer fitted with the paddle attachment, mix together the all-purpose flour, almond flour, baking powder, and salt.
With the mixer running on medium speed, add in the butter slices one at a time. Mix until fully incorporated and no butter chunks remain, around 1 to 2 minutes.
Add in the egg and vanilla, then mix on low until everything comes together into a smooth dough.
Divide the dough into two, then press half into the prepared baking pan and spread into a smooth and even layer. Shape the remaining half of dough into an 8×8 inch square on a separate piece of parchment paper and set aside.
Scatter the prepared filling over the shortbread in the pan and pat into an even layer.
Carefully flip the other half of dough on top of the filling layer and peel back the parchment paper, using an offset spatula or knife to carefully scrape away the paper if it sticks. If needed, smooth the surface of the cookie bars.
Bake for around 40 minutes, or until the shortbread is puffed, set, and matte on top and the edges are golden brown.
Remove the pan from the oven and allow to cool fully before lifting out the shortbread.
Once the bars have completely cooled, prepare the icing by mixing together the powdered sugar, cinnamon, vanilla, and salt. Stir in the milk until a smooth glaze forms, adding more milk or powdered sugar to adjust the consistency as needed.
Immediately pour the icing over the shortbread bars and spread into an even layer. Sprinkle over flaky salt, if desired, then let the glaze set completely before slicing and serving.
These shortbread bars are best enjoyed the day of, but leftovers can be stored in an airtight container at room temperature for 3 to 4 days.