Preheat oven to 350 degrees. In a medium bowl, whisk together oats, flour, raisins, baking soda, and salt; set aside. Using an electric mixer, beat butter and sugars until light and fluffy, scraping down bowl as necessary. Add egg and vanilla; beat until combined. Gradually add oat mixture; beat just until combined.
Drop dough by rounded tablespoonfuls, 2 inches apart, onto two baking sheets. Bake until cookies are golden brown but still soft, 12 to 16 minutes, rotating sheets halfway through. Cool 5 minutes on sheets; transfer cookies to a wire rack to cool completely.
To make the Oatmeal Craisin Cookies as seen on "The Martha Stewart Show," substitute 1/2 cup dried cranberries (Craisins) for 1/2 cup of raisins.