Place butter in large skillet and allow to melt until lightly brown.
In a large bowl, combine browned butter, white sugar, and brown sugar. Whisk until smooth and glossy.
Add the egg and vanilla extract, mixing until fully incorporated.
Stir in baking soda, flour, and salt until a soft dough forms. Do not overmix.
Fold in dark chocolate chips and semi-sweet chocolate chunks.
Cover and refrigerate the dough for 30 minutes.
Preheat the air fryer to 315°F (157°C) for 3–5 minutes.
Scoop dough into 11⁄2-tablespoon portions and flatten slightly.
Line the air fryer basket with a single sheet of parchment paper.
Arrange cookies in a single layer, leaving space between each.
Air fry for 8–10 minutes, or until edges are golden and centers are set.
Let cookies cool in the basket for 5 minutes before transferring to a wire rack.