Preheat oven to 320°F / 160°C and line a baking sheet with parchment paper.
Add the sugar, egg and vanilla to a bowl and whisk until pale and frothy (about 20 seconds of whisking by hand). There's really no need for a stand mixer or electric mixer for this recipe as it comes together so easily.
Melt the butter in the microwave in 30 second increments, then add it to the sugar/egg mixture and whisk, just until combined.
Pour in the oats, flour, baking powder and salt and stir everything together. I recommend switching to a spoon for this so the mixture doesn't get stuck in your whisk.
Scoop a heaped teaspoon of cookie dough onto your baking sheet. It will look more like a blob than a perfect ball, but that's okay as it will spread out into a circle in the oven.
Bake for 12 minutes. You'll know the cookies are ready as they will have spread out into a thin, lacy cookie and the edges will be golden brown. The middle will still look a little underdone, but they will continue to bake a little as they cool.
Let the cookies sit on the cookie sheet for 10 minutes before transferring to a wire rack to cool completely.
Notes
Type of Oats - I used quick oats for my cookies, but you could also use rolled oats for chunkier cookies or instant oats for finer cookies. Perfectly round cookies - the cookies should spread into a perfect circle, but if they aren't perfect and you'd like them to be, you can use a round cookie cutter to gently scoot the edges in while they are still warm!