Mix oats and brown sugar, mix in butter and vanilla.
Divide mixture evenly in 2 ungreased 8-inch square pans, spreading evenly, or in a single pan for thicker, more chewy squares. Bake at 375F for about 10 minutes (15 minutes if in a single pan) or until golden-brown. Squares will be soft, but will harden when cool.
Allow to cool for 5 minutes, then mark in squares with a sharp knife. Loosen edges and allow to cool before removing from pans.