Preheat oven to 350 degrees. Line baking sheet with parchment paper or Silpat. Whisk flour, baking powder, baking soda, and table salt in a medium bowl.
Beat butter and sugars until light and fluffy. Scrape down bowl with rubber spatula, then add egg and vanilla and beat until incorporated. Scrape down bowl again. Add flour mixture gradually and mix until just incorporated and smooth. Gradually add oats and white chocolate and mix until well incorporated.
Divide dough into 24 equal portions, each about 2 tablespoons. Roll between palms into balls, then place on lined baking sheets about 2 1/2 inches apart. Using fingertips, gently press down each ball to about 3/4-inch thickness.
Sprinkle a pinch or two of sea salt on each cookie
Bake until cookies are deep golden brown, about 13 to 16 minutes, rotating baking sheet halfway through. Transfer baking sheet to wire rack to cool.