Beat butter until creamy; add sugars and beat until blened. Add vanilla and egg; beat well.
Sift together flour, salt, soda, cinnamon, and nutmeg. Add to creamed mixture alternately with milk; then stir in oats. Pour batter into greased and floured pan (8-inch square glass baking dish). Bake for 40-50 minutes and leave in pan.
FROSTING: Combine in a saucepan and boil until frosting bubbles. Spread on cake.