In a medium saucepan, melt the butter and let it simmer until the milk solids start to brown at the bottom. It will start to foam and it will be a medium honey color. Remove from heat and transfer to a heat-proof bowl and let solidify in the refrigerator.

Preheat the oven to 350 F and line a cookie sheet with parchment paper and set aside.

In a stand mixer, beat chilled brown butter, softened butter, granulated sugar, and brown sugar until combined and fluffy, about 2 minutes.

Add the egg, egg yolks, and vanilla extract then mix until just combined.

In a medium bowl, whisk the all-purpose flour, cake flour, baking powder, baking soda, and salt. Add this dry mixture to the stand mixer with the wet ingredients. Mix until fully combined.

Pour about 3 tablespoons of cinnamon sugar onto a small plate and set aside. If you don't have cinnamon sugar on hand, mix 2 tbsp of granulated sugar with 1 tbsp of cinnamon.

Using a 2 tablespoon cookie scoop, take a full scoop of dough and in between your hands, flatten it out a bit (to where it's about 1/2 inch thick) and dip both sides into the cinnamon sugar mixture. Form the dough into a ball, where it should look like the cinnamon is marbled throughout. Place on the cookie sheet and gently flatten it with your fingers until the "disc" is approximately 2 1/4 inches in diameter. Repeat while spacing out the dough "discs" about 3 to 4 inches from each other.