Combine pineapple juice and apricots in a small saucepan; bring to a boil. Reduce heat; simmer 8 minutes or until plump. Drain apricots in a colander over a bowl, reserving 1/3 cup pineapple juice.
Melt margarine in a 9-inch cast-iron skillet over medium heat. Spoon 1 tablespoon melted margarine into a small bowl; set aside. Add reserved pineapple juice and brown sugar to margarine in skillet. Bring to a boil; cook 1 minute or until slightly thick. Sprinkle apricots and walnuts over brown sugar mixture; set aside.
Combine flour and baking powder in a bowl. Add 1/4 cup granulated sugar, milk, egg yolk, and vanilla to margarine in bowl; stir well. Add to flour mixture, stirring well; set aside. Beat egg whites at high speed of a mixer until foamy. Gradually add 1/4 cup granulated sugar, 1 tablespoon at a time, beating until stiff peaks almost form. Gently stir one-fourth of egg white mixture into batter; gently fold in remaining egg white mixture. Pour batter over apricot mixture in skillet.
Bake at 350° for 30 minutes or until a wooden pick inserted in center comes out clean. Let stand 5 minutes on a wire rack. Loosen cake from sides of skillet, using a narrow metal spatula. Invert onto a cake plate; cut into wedges.