In a small saucepan, melt the butter over medium heat. Whisk constantly until it starts to foam and turn golden brown. The nutty aroma is your cue to remove it from the heat. Transfer it to a bowl and let it cool.

In a large bowl, combine the cooled browned butter, brown sugar, and granulated sugar. Beat until smooth. Add the egg, egg yolk, and vanilla extract, mixing until well combined.

In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry mixture to the wet ingredients, mixing until just combined.

Cover the dough and refrigerate for at least 30 minutes. This step enhances the flavor and helps the cookies hold their shape during baking.

Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper. Scoop the dough into 1-ounce balls and place them 2 inches apart. Bake for 11 minutes, or until the edges are golden brown and the centers are slightly puffed.

Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack. Serve warm or store in an airtight container.