Place racks in upper and lower thirds of oven; preheat to 375°.
Whisk 1½ cups plus 1 Tbsp. (200 g) all-purpose flour, 1¼ tsp. (4 g) Diamond Crystal or ¾ tsp. (4 g) Morton kosher salt, and ¾ tsp. (4 g) baking soda in a small bowl; set flour mixture aside.
Cook ½ cup (1 stick; 113 g) unsalted butter in a large saucepan over medium heat, swirling often and scraping bottom of pan with a heatproof rubber spatula, until butter foams, then browns, about 4 minutes.
Scrape melted butter and any brown bits to a large heatproof mixing bowl and let cool 1 minute.
Cut remaining ¼ cup (½ stick; 56 g) unsalted butter into small pieces and add to brown butter.
Once butter is melted, add 1 cup (200 g) (packed) dark brown sugar and ¼ cup (50 g) granulated sugar and whisk, breaking up any clumps, until sugar is incorporated and no lumps remain.
Add 1 large egg and 2 large egg yolks and whisk until sugar dissolves and mixture is smooth, about 30 seconds.
Whisk in 2 tsp. vanilla extract.
Using rubber spatula, fold reserved dry ingredients into butter mixture just until no dry spots remain, then fold in 6 oz. (170 g) bittersweet chocolate.
Using a 1½-oz. scoop (3 Tbsp.), portion out 16 balls of dough and divide between 2 parchment-paper-lined rimmed baking sheets.
Bake cookies, rotating sheets if cookies are browning very unevenly, until deep golden brown and firm around the edges, 8–10 minutes.
Let cool on baking sheets.
