Preheat oven to 360F. Line two baking sheets with Silpats or baking paper.
Mix flour, baking powder, baking soda, and salt together in a medium bowl.
Beat the butter and both sugars in a food mixer on medium for a few minutes. Add the egg and vanilla and mix for a minute on low speed.
Remove bowl from mixer, add the flour in batches and stir with a wooden spoon until the mixture is just incorporated. Add the oats and white chocolate and stir again.
Depending how large you like your cookies, measure out the dough into 1 1/2 to 2 tablespoon pieces. (I made mine on the smaller side.)
Roll into balls, place on the Silpat sheets and flatten slightly.
Sprinkle a little sea salt on each cookie.
Bake until cookies are golden brown, about 16 - 18 minutes, rotating baking sheets halfway through. Remove from the oven, let sit for a couple of minutes, then transfer the cookies to wire racks to cool.