Add the butter to a saucepan and cook over medium heat, stirring often, until melted, nutty-smelling, and golden bits form on the bottom. Remove from heat and let cool for about 10 minutes.
Pour the brown butter into a mixing bowl and whisk in the brown sugar and granulated sugar until smooth and well combined.
Mix in the egg, egg yolk, and vanilla extract until fully incorporated.
Add the flour, baking soda, and salt and stir just until combined, being careful not to overmix.
Fold in the chocolate chips or chunks.
Cover and chill the dough for 30 minutes to help control spreading.
Preheat the oven to 350°F and line a baking sheet with parchment paper.
Scoop the dough into balls and place them on the baking sheet, spacing them a few inches apart.
Bake for 10–12 minutes, until the edges are set and lightly golden but the centers still look soft.
Let the cookies cool on the baking sheet for 5 minutes, then transfer to a cooling rack to cool completely.
Notes
*Cool the butter slightly: Let the browned butter sit for a few minutes before mixing. If it’s too hot, it can make the dough greasy and cause the cookies to spread more than you want.*Don’t skip the chill: That short chill time really helps the dough hold its shape. Even 30 minutes makes a difference, especially if your kitchen is warm.*Underbake slightly: Pull the cookies when the centers still look soft. They’ll finish setting as they cool, which keeps them from drying out.*Use a cookie scoop: Even portions mean even baking. A scoop makes things easier, but a spoon works if you keep the sizes consistent.*Add extra chocolate on top: Press a few chips or chunks into the dough before baking. It makes the cookies look better and adds extra chocolate in every bite.