Preheat oven to 350°F (177°C). Line a large baking sheet with parchment paper or a silicone baking mat.
In a medium-sized saucepan over medium heat, melt the butter. Continue to cook the butter, stirring constantly, until it starts to turn golden brown and has a nutty aroma. Remove from heat and set aside to cool.
In a large bowl, whisk together the granulated sugar, brown sugar, egg, and cooled melted butter until combined. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add to the wet ingredients, stirring until combined.
Drop the cookie dough onto the prepared baking sheet. Bake for 10-12 minutes, or until golden brown. Remove from oven and let cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Interesting Facts
Brown butter is made by heating butter until the milk solids turn golden brown.
Cookies made with brown butter have a deeper, nuttier flavor than regular cookies.
These cookies are best eaten the day they are made, but can be stored in an airtight container for up to 3 days.