Preheat oven to 350 degrees. In a blender or coffee grinder, process ¾ cup oats into a fine meal. Whisk together ground oats, cornstarch, cinnamon, baking powder, and salt.
In a large bowl, using a mixer, beat butter and sugars until light and fluffy. Beat in egg and vanilla. With mixer on low, gradually add oat mixture, beating until combined. Fold in raisins, and remaining oats.
In batches, drop dough in 2-tablespoonful mounds onto a parchment-lined baking sheet, 2 inches apart. Bake until cookies are golden brown at edges, 15 to 18 minutes. Let cool on sheet on a wire rack 2 minutes, then transfer to rack and let cool completely.
Notes
Thanks to Tywana who did some experimenting with oat flour and found that you can substitute 1 cup of oat flour for every 1 ⅓ to 1 ½ cups oats. Tywana also noted that adding a little xanthan gum kept the cookies from getting hard.