Preheat the oven to 350 degrees F. Spray an 8x8 inch pan with nonstick spray.
Blend the flour, sugar and salt in food processor. Add the butter gradually and process until coarse crumbs form. (If you do not have a food processor, you can do this by hand by cutting the butter into the dry ingredients until crumbs form).
Press the crumbs onto the bottom of the prepared dish. Bake until the center is golden, about 25 minutes. Keep the oven heated.
APRICOT LAYER
While the shortbread layer is baking, prepare the apricot layer. Place the apricots in a small saucepan, and add enough water to cover them. Boil until soft, about 4 minutes. Drain and set aside.
Sift the flour, baking powder, and salt into small bowl. In a separate, large bowl, beat the eggs with an electric mixer. Add the brown sugar and vanilla, and beat until thickened. Stir in the flour mixture, then nuts and drained apricots.
Gently spread over the baked shortbread layer. Bake the bars until they are puffed and dark brown. A toothpick inserted into the middle should come out with a few crumbs attached, about 35 minutes. Cool completely before cutting.
Cut uniformly into desired size. Transfer to waxed paper or rack with paper towels underneath. Sift powdered sugar over bars.