Preheat oven to 350 degrees. Line or grease an 8x8 pan. 

In a bowl, whisk together flour, powdered sugar, and salt. 

Mix in butter using a pastry cutter or 2 knives. Mixture should crumbly forming small pea sized clumps of dough. 

Press shortbread into pan evenly, and bake for 10-15 minutes or until the edges are beginning to brown. Remove from oven and set aside to cool slightly. 

While crust is cooling, make the filling. Whisk brown sugar, egg, and vanilla until smooth. 

Stir in flour, baking soda, and salt and mix until smooth. 

Stir in chopped walnuts. 

Pour into pan and spread evenly. Bake for 25 minutes, until the surface looks dry and the filling has set and risen slightly. Cool completely, then cut into small squares.