1. In 1-quart saucepan over high heat, heat apricots and enough water to cover to boiling. Reduce heat to low; cover and cook apricots 15 minutes; drain. Finely chop apricots; set aside.
2. Preheat oven to 350°F. Grease 8" by 8" baking pan. Into large bowl, measure butter or margarine, sugar, and 1 cup flour. With mixer at medium speed, beat until well mixed (mixture will be crumbly). Pat dough evenly into pan. Bake 25 minutes or until golden.
3. Meanwhile, in same bowl, combine apricots, brown sugar, next 5 ingredients, and 1/3 cup flour. With mixer at medium speed, beat until mixed, scraping bowl often.
4. Remove baking pan from oven; pour apricot mixture over baked layer and return to oven; bake 25 minutes or until golden. Cool completely in pan on wire rack. When cold, cut into 16 squares. Sprinkle with confectioners' sugar. Store in tightly covered container.