Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the oats, flour, baking soda, and salt until well combined.
In a separate large bowl, beat the softened butter, granulated sugar, and brown sugar together with a hand mixer or stand mixer until light and fluffy, about 2–3 minutes.
Add the egg and vanilla extract to the butter mixture, and beat until fully incorporated.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. The dough will be thick and slightly crumbly.
Scoop tablespoon-sized portions of dough onto the prepared baking sheet, spacing them about 2 inches apart. Gently flatten each cookie with the back of a spoon or your fingers.
Bake for 10–12 minutes, or until the edges are lightly golden but the centers are still soft. The cookies will firm up as they cool.
Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.