Start by melting the butter in a small saucepan over medium heat. Stir occasionally until it starts to foam and the milk solids turn brown, then immediately remove from the heat. This step usually takes about 3-5 minutes.
Place the butter in a mixing bowl and let it cool for about 5 minutes. Alternatively, you can place it in the refrigerator for a couple of minutes.
Stir the brown sugar, granulated sugar, milk, and vanilla extract into the butter.
Gently fold in the flour, baking soda, and pinch of salt until the mixture is almost combined, with a few dry spots still visible.
Fold in the chocolate chips, then shape the dough into a ball or disc. Wrap dough in plastic wrap or put a cover over it, then refrigerate for about 10 minutes so it can firm up a bit.
Preheat air fryer to 325°F (approx. 165°C).
Divide dough in two, shape them into discs, and place them on top of parchment paper.
Air fry for 8 minutes, then leave the cookies in the air fryer for 3-5 minutes after the timer goes off.
Lift the cookies out of the air fryer basket by holding the edges of the parchment paper. Let them cool for a few minutes, then transfer to a wire cooling rack so they can continue cooling and setting. Enjoy!