Heat oven to 350 degrees. Line baking sheets with parchment paper. Whisk flour, baking powder, baking soda, and salt together in bowl.
Using stand mixer fitted with paddle, beat butter and both sugars at medium low speed to medium and continue to beat until pale and fluffy, about 1 minute. Scrape down bowl as needed.
Add egg and vanilla extract and beat on medium low until fully incorporated, about 30 seconds. Reduce speed to low, add flour mixture, and mix until just incorporated and smooth, about 10 seconds. With mixer running, gradually add oats and mix until well incorporated, about 20 seconds. Give dough final stir by hand to ensure that no flour pockets remain and ingredients are evenly distributed.
Working with 2 tablespoons of dough at a time, roll into balls and space them 2 1/2 inches apart on prepared sheets. Bake 1 sheet at a time, until cookies are golden brown and crispy on the edges. Let cookies cool on wire rack.
