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 190 degrees C.
Drop dough by tablespoonfuls onto lightly greased baking trays. Flatten biscuits slightly and bake for 10 minutes. Do not overbake.
Take biscuits from the oven when still puffy and edges are just beginning to brown. Let biscuits cool a minute or two on baking trays before removing. Cool completely on racks. They are fragile and difficult to remove from the baking trays when they are still warm, so work gently.