Preheat oven to 350 F. In a medium bowl, whisk together flour, oats, salt, and baking soda. In a large bowl using a mixer, beat softened butter with brown sugar until fluffy.
Add in egg and vanilla extract and beat until smooth. Add the flour and oat mixture in three separate batches, beating until fully incorporated. Roll cookie dough into balls and place 2-inches apart onto ungreased baking sheets. Bake for 10-12 minutes.