Preheat the air fryer to 370°F for 5 minutes while you prepare the dough.
In a medium bowl, whisk the melted, slightly cooled butter and the brown sugar together until well combined.
Add the egg yolk and vanilla extract to the bowl and whisk until incorporated.
Add the all-purpose flour and baking soda. Stir just until no large lumps of flour remain—do not overmix.
Fold in the semisweet chocolate chunks until evenly distributed.
Line the air fryer basket with parchment paper cut to fit. Use a 1.5-tablespoon scoop to portion the dough into six balls for the first batch, placing each ball at least 2 inches apart in the basket so they do not touch.
Air fry at 370°F for 6–8 minutes, or until the cookies are golden brown around the edges and the tops look set.
Carefully transfer the cookies to a wire rack to cool. If you have more dough, repeat steps 6–7 with subsequent batches.
Serve warm or at room temperature. Store any remaining cookies in an airtight container at room temperature for up to three days.