In a heavy medium saucepan melt margarine or butter. Add apples; cook over medium heat about 2 minutes or until tender. Remove apple mixture from pan; set aside.
In the same saucepan combine brown sugar and cornstarch. Stir in half-and-half or light cream and corn syrup. Cook and stir until thickened and bubbly (mixture may appear curdled). Cook and stir for 2 minutes more. Remove from heat. Stir in apple mixture, nuts, and vanilla. Serve warm. Cover and refrigerate remaining sauce for up to 24 hours. Makes 1-3/4 cups.