In a mixing bowl, combine the all-purpose flour, cocoa powder, granulated sugar, baking powder, baking soda, and salt. Whisk together until well mixed.

In another bowl, mix the melted butter, egg, whole milk, and vanilla extract. Whisk until combined.

Gradually add the wet ingredients to the dry ingredients, stirring gently until smooth and combined. Do not overmix.

Lightly grease the small cake pan with cooking spray or butter. Pour the batter into the prepared pan and smooth the top with a spatula.

Preheat the air fryer to 320°F (160°C). Once preheated, place the cake pan inside the air fryer basket.

Cook for 12-15 minutes, or until a toothpick inserted into the center comes out clean. Once done, remove the cake from the air fryer and allow it to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.

While the cake is cooling, prepare the brown butter frosting. In a saucepan over medium heat, melt the butter. Continue cooking, stirring frequently, until the butter turns a deep golden brown and develops a nutty aroma (about 5-7 minutes).

Once browned, remove the butter from the heat and let it cool slightly. In a bowl, combine the brown butter, powdered sugar, milk, and vanilla extract. Whisk until you reach a smooth, spreadable consistency.

Once the cake has completely cooled, spread the brown butter frosting over the top of the cake using a spatula.