Cream the butter and sugar together until the mixture is thoroughly blended, Add the vanilla and beat until fluffy.
In a bowl, stir together the flour, oatmeal, baking soda, salt and nutmeg and add to the butter and sugar mixture. Beat until well blended.
With a teaspoon, drop the batter onto a baking sheet and flatten the balls of batter with a fork that has been dipped in cold water. Bake at 350F for 8-10 minutes. Start checking on the cookies at 8 minutes. Remove when they are golden brown,.