Cream first three ingredients until fluffy, add eggs and vanilla. Mix all dry ingredients into butter mixture. Stir in oats. Let dough stand at room temperature for 2 hours.
Preheat oven to 375 degrees F (190 degrees C).
Drop dough by tablespoonfuls onto lightly greased cookie sheets. Flatten cookies slightly and bake for 10 minutes. Do not overbake.
Take cookies from the oven when still puffy and edges are just beginning to brown. Let cookies cool a minute or two on cookie sheets before removing. Cool completely on racks. They are fragile and difficult to remove from the cookie sheets when they are still warm, so work gently.