These are large, bakery-style thick cookies. They are soft and chewy with crispy edges and have a delicious nutty caramel flavor from the browned butter and brown sugar.
Melt the butter in a small saucepan over medium-low heat. Cook about 10 minutes, stirring occasionally, until butter starts to foam and turn brown. Immediately pour into the bowl of your stand mixer, and set aside to cool for 10 minutes.
Combine the flour, baking powder, baking soda and salt, and set aside.
In the bowl of a stand mixer with the paddle attachment, add the brown sugar and granulated sugar. With the mixer on medium-high speed, slowly add the browned butter and mix for about three minutes, until well combined.
Add the egg, egg yolks and vanilla; beat on medium speed until well combined.
With the mixer running on low speed, gradually add the flour mixture, beating just until combined, about a minute. Fold in the chocolate (and nuts if using).
Roll a scant ¼-cup of the dough into a ball. Hold the dough ball with the fingertips of both hands, and pull into two equal halves. Rotate the halves 90 degrees and, with jagged surfaces facing up, join the halves together at their base, again forming a single ball, being careful not to smooth the dough's uneven surface.
Refrigerate the dough for at least an hour. It's even better if you can wait longer or overnight.
Adjust the oven racks to the upper- and lower-middle positions, and preheat oven to 325 degrees. Line two baking sheets with parchment paper.
Place the formed dough balls on the prepared baking sheets, jagged surface up, spacing them 2½ inches apart. Sprinkle with flaky sea salt, if desired.
Bake for about 15-18 minutes, until the cookies are light golden brown, and the edges start to set, but the centers are still a bit soft and puffy. Rotate the baking sheets halfway through the baking time. Cool the cookies on the baking sheets. Once cool, store in an airtight container at room temperature for up to four days.