Place oven rack in the middle position. Preheat the oven to 350°F. Line 2 baking sheets with parchment paper and set aside.
In a medium bowl, whisk together 1 ¾ cups all-purpose flour, salt, baking soda, and baking powder. Set dry ingredients aside.
2 cups all-purpose flour, 1 teaspoon salt, ¾ teaspoon baking soda, ¼ teaspoon baking powder
Brown the butter: In a large saucepan, add unsalted butter and cook over medium heat, swirling often and scraping bottom of pan with a heatproof rubber spatula, until butter foams, then turns dark brown and smells nutty, about 6–8 minutes.
brown butter
Add the remaining ¼ cup all-purpose flour to the brown butter. The butter will foam immediately, but don’t worry; just keep stirring. Cook, stirring constantly, until the mixture is deep golden brown (the shade of a chai latte), about 2 minutes.
Scrape the brown butter mixture, including any browned bits at the bottom of the pan, into a medium heat proof mixing bowl.
To the brown butter flour mixture, add the dark brown sugar and whisk until no large lumps remain.
1 ¼ cups dark brown sugar
Add the whole egg, egg yolk, and vanilla extract and whisk vigorously until sugar is dissolved and mixture is smooth and paler in color, about 1 minute.
1 large egg, 1 large egg yolk, 2 teaspoons vanilla extract
Using a rubber spatula, add the dry ingredients and fold in until no dry spots remain. The dough will be thick and maybe even look a little greasy.
Cover the dough and let rest at room temperature for 20 minutes. Allowing the dough to rest ensures thicker cookies.
If making medium cookies, using a #16 cookie scoop (about ¼ cup), portion out 12 balls of dough (about 56 g each).If making large cookies, using a #10 cookie scoop (about 6 heaping Tbsp.), portion out 8 balls of dough (about 85 g each). Divide the dough balls between the two prepared baking sheets. Bake one tray of cookies at a time until firm and golden brown around the edges, 9–11 minutes for medium cookies, 10–12 minutes for large cookies. Let the cookies cool on baking sheets.