Cream butter and sugar together. Beat in egg and vanilla and set aside. Combine flour, baking soda, cinnamon, salt and nutmeg; gradually add to creamed mixture. Fold in apples. Pour into a greased 8x8 baking pan. Bake at 350 for 40-45 minutes. Serve warm with butter sauce.
Melt butter in a saucepan; stir in sugar, brown sugar and half and half. Bring to a boil over med. heat, stirring constantly. Reduce heat; simmer, uncovered for 15 minutes, stirring occasionally.