Place racks in upper and lower thirds of oven and preheat to 375°. Whisk flour, baking powder, kosher salt, and baking soda in a medium bowl; set aside.
Using an electric mixer on medium speed, beat butter, brown sugar, sugar, and powdered sugar until light and fluffy, 3-4 minutes. Add egg yolks, egg, and vanilla.
Beat, occasionally scraping down the sides of the bowl, until mixture is pale and fluffy, 4-5 minutes. Reduce mixer speed to low; slowly add dry ingredients, mixing just to blend. Using a spatula, fold in chocolate.
Spoon rounded tablespoonfuls of cookie dough onto 2 parchment paper-lined baking sheets, spacing 1-inch apart. Sprinkle cookies with sea salt.
Bake cookies, rotating sheets halfway through, until just golden brown around the edges, 10-12 minutes (the cookies will firm up as they cool). Let cool slightly on baking sheets, then transfer to wire racks; let cool completely.