Generously grease and flour a 10-inch fluted tube pan (10- to 12-cup); set aside. In medium bowl combine flour, baking powder, salt, and baking soda; set aside.
In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds; beat in brown sugar until well combined. Add eggs and molasses; beat well (mixture will look curdled). Stir in pie filling and apricots. Add flour mixture all at once to pie-filling mixture; stir until well combined.
Spoon batter into prepared pan. Place pan on rack in Dutch oven containing 1 inch of water. Cover tube pan with foil; press foil tightly against rim of pan.
Bring water to boiling; reduce heat. Cover Dutch oven; steam for 1-3/4 to 2 hours or until a wooden toothpick inserted near center comes out clean. Carefully add additional boiling water as needed to maintain water level.
Remove pan from Dutch oven; remove foil. Cool cake in pan on wire rack for 30 minutes. Invert cake onto serving plate; remove pan. Wrap cooled cake in foil; refrigerate up to 10 days. Makes 10 to 12 servings.
Preheat oven to 350 degrees F. Place chilled foil-wrapped cake on baking sheet. Bake 40 minutes or until warmed through. Cool slightly. Serve warm with desired sauce.