Mix the dry ingredients. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
Make the egg mixture. In a liquid measuring cup, whisk together the egg, egg yolk, and vanilla.
Cream the butter and sugars, then add the egg mixture in three parts. In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugars. Beat on medium-high until light, fluffy, and doubled in volume, 2 to 3 minutes, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary. Reduce the mixer to low, add the egg mixture in three equal additions, only adding the next addition when the previous is fully incorporated. Scrape down bottom and sides of the bowl. Add the dry ingredients, then the chocolate. With the mixer on low, gradually add the dry ingredients and beat until just combined. Add the chocolate all at once and beat on medium-low until the chocolate is evenly distributed throughout, about 1 minute.
Assemble the cookies for chilling, then chill overnight. Use a 3-Tablespoon cookie dough scoop to portion the cookie dough into balls, placing them next to each other on the prepared sheet pan as you go. Cover the pan loosely with plastic wrap and refrigerate for at least 2 hours, preferably overnight. Thaw the chilled cookie dough while you preheat the oven. When ready to bake, line two half sheet pans with parchment paper. Place the chilled cookie doughs at least 3 inches apart on the prepared sheet pans. Position racks in the upper third and lower third positions in the oven and preheat to 375°F.
Bake the cookies. Before baking, flatten each cookie dough ball with the palm of your hand until each cookie is roughly ¾ inch thick. Place one sheet pan on each oven rack and bake for 16 to 18 minutes, swapping their positions halfway through the Bake Time. The cookies are done when their edges have set but the centers are still gooey. Cool the cookies on the pan on a wire rack for 20 minutes, or until the edges and bottoms of the cookies have set and feel firm to the touch. Serve and store. Serve warm or at room temperature. The cookies can be stored in an airtight container or zip-top bag at room temperature for up to 3 days.