Brown the butter in a light-colored skillet over medium heat, whisking occasionally, until lightly browned with a nutty aroma; pour into a heat-proof bowl and allow to cool for 5 minutes.

Whisk the flour, baking soda, and salt together in a medium bowl; set aside.

Add the granulated sugar and brown sugar to the cooled brown butter; beat on medium-high speed using a mixer until combined, about 1 minute.

Beat in the egg and vanilla extract.

Gradually add the dry ingredients into the wet ingredients, mixing on low speed and then increasing to high speed until combined; the dough will be thick.

Roll the dough into balls, about 1 tablespoon each, and dip the tops in sprinkles; place on a lined baking sheet and chill in the refrigerator for 30 minutes.

Preheat oven to 350°F (177°C) and line large baking sheets with parchment paper or silicone baking mats.

Line the chilled dough balls on baking sheets about 3 inches apart; bake for 12–13 minutes or until lightly browned on the sides.

Remove from the oven and cool on the baking sheet for 5 minutes before transferring to a cooling rack to cool completely.