Preheat oven to 325 degrees F (165 degrees C). Cover baking sheets with foil, then coat the foil with a non-stick cooking spray.
In a medium bowl, combine oats, flour, salt, and baking powder. In a large bowl, cream sugar and butter until fluffy. Beat in egg and vanilla. Mix in the flour and oat mixture until just combined. Drop dough by teaspoonfuls onto the prepared baking sheets, 2 1/2 inches apart.
Bake at 325 degrees F (165 degrees C) for 10 to 12 minutes, or until edges turn golden. Cool, then peel cookies off with your fingers. Be sure to re-spray baking sheets with non-stick cooking spray between batches.
