Preheat oven to 350 degrees F & grease an 8-inch square baking dish.
In a small saucepan, cook apricots in water over medium heat for 10 minutes or until softened, then drain, cool & chop, before setting aside.
In a large bowl, cream butter & powdered sugar until light & fluffy, then gradually add 1 cup of the flour until well blended.
Press into the prepared baking dish & bake for 20 minutes or until lightly browned.
Meanwhile, in a small bowl, beat eggs & brown sugar until blended.
In another small bowl, whisk together the baking powder, salt & the remaining 1/3 cup of flour, then gradually add this flour mixture to the egg mixture.
Beat in the vanilla, then stir in the apricots & nuts before pouring this mixture over the crust.
Bake for 30 minutes or until set, then cool on a wire rack.
When cooled, if desired, dust with powdered sugar, then cut into bars. Store any left-over bars in the refrigerator.