Preheat the oven to 325 and line a square 8x8 pan with a sheet of parchment. In a stand mixer, cream the butter until light and fluffy. Add the powdered sugar and vanilla and mix well again. In a bowl, whisk the flour, almond flour and salt. Add the egg to the mixer and scrape the sides, then mix until well combined.
Add the dry ingredients and mix on low until combined. Finish mixing with a rubber spatula to ensure it is well mixed, but don't over mix the dough. Press 1/2 the dough into the bottom of the pan. Use an offset spatula to spread it out. It will be sticky so you can oil your hands or the spatula to spread it if needed.
Combine the ingredients for the filling in a bowl and mix well. Spread this over the shortbread. Gently spread the rest of the dough over the filling and smooth it out. Bake for 40-45 minutes until it is no longer raw in the center and is golden brown. Let rest for 30 minutes, then remove from the pan.
Mix the icing ingredients in a bowl until smooth. Spread over the top and when fully cooled, cut into squares.