Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the rolled oats, all-purpose flour, baking soda, and salt until well combined.
In a large bowl, mix the melted butter, granulated sugar, and light brown sugar until smooth and creamy.
Add the egg and vanilla extract to the butter and sugar mixture and beat until fully incorporated.
Gradually add the dry oat mixture to the wet ingredients, stirring until just combined.
Scoop about 1 tablespoon of dough per cookie onto the prepared baking sheets, spacing them about 2 inches apart. Flatten each cookie slightly with the back of a spoon or your fingers to encourage crispiness.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are golden brown and the centers are set.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely. This helps them crisp up further.
Store the cooled cookies in an airtight container at room temperature.