Prepare brown butter by melting pats of butter in a skillet over medium-low heat until foamy, milk solids begin to sink to the bottom, and butter smells nutty. Pour into heatproof measuring cup (you should have one cup) and chill in the fridge at least 4 hours or overnight.
1 cup brown butter
Preheat the oven to 350°F. Line two baking sheets with parchment paper. Set aside
In a medium bowl, combine the all-purpose and cake flours, baking soda, baking powder, and salt in a large mixing bowl. Set aside.
1 ¼ cups all-purpose flour, 1 ¼ cups cake flour, 1 teaspoon baking soda, ½ teaspoon baking powder, 1 teaspoon salt
In the bowl of a stand mixer, cream together the brown butter, granulated sugar, and brown sugar on medium speed until light and fluffy, about 3-5 minutes.
1 cup brown butter, 1 cup granulated sugar, ¼ cup dark brown sugar
Add in the egg and vanilla and mix until well combined, scraping down the sides and bottom of the bowl as needed.
1 large egg, 2 teaspoons vanilla extract
With the mixer on low, stir in the dry ingredients just until the dough is well combined. Do not over mix.
Scoop dough into 1 ½ tablespoon sized balls. Gently roll between your palms into a smooth ball and roll in sugar to coat. Set on prepared baking sheets about 2 inches apart.
¼ cup granulated sugar
Bake the cookies in preheated oven for 11-12 minutes or until they are just starting to turn golden brown on the edges. Do not overbake.
Remove from the oven and allow to cool on baking sheets for 5 minutes then transfer to a wire rack to cool completely.