Heat butter in a small saucepan over medium heat until melted, about 2 minutes. Continue to cook, swirling pan constantly until butter is dark golden brown and has nutty aroma, 1 to 3 minutes. Browned butter can burn easily and does not taste good burnt so watch it carefully. There is a certain smell it gives off when it starts to brown that is hard to describe, but once you do it once, you will know. Immediately pour into your mixing bowl and scrape all the browned bits in too.
Heat the oven to 350 degrees F. Line 2 large baking sheets with parchment paper, or lightly coat them with cooking spray.
Add the brown sugar (mix the 1/4 cup brown sugar + granulated in a small bowl on the side to coat your cookies in), salt, baking soda and mix well.
Add the egg and yolk and whisk well until incorporated. Add the baking powder and whisk again until very well mixed.
Add the flour mix until just combined, about 1 minute. Give the dough a final stir with a rubber spatula to ensure that no flour pockets remain and the ingredients are evenly distributed.
Divide the dough into 24 portions, each about 2 tablespoons. I use a cookie scoop. Working in batches, toss the balls in the reserved sugar mixture to coat and set them on the prepared baking sheet, spacing them about 2 inches apart.
Bake one sheet at a time until cookies are browned and still puffy and edges have begun to set but the centers are still soft (cookies will look raw between cracks and seem underdone – don’t overbake), 9-13 minutes. Cool the cookies for 1-2 minutes on the baking sheets and then remove to a wire rack to cool completely.