In a large bowl, using an electric mixer fitted with a paddle or whisk attachment, cream the butter, sugar, and brown sugar on medium-high speed for 2-3 minutes. Then add the egg yolk and vanilla and mix for about 1 minute, until creamy and well combined.
Add the flour, baking soda, and salt, and mix on medium-low speed just until incorporated, about 30-60 seconds. Then add the chocolate chips and mix on medium-low speed just for a few seconds until well distributed. Then cover and chill for 1 hour.
Preheat the air fryer at 350°F (175°C). Prepare parchment paper for the air fryer basket by cutting it into the size of the air fryer basket. Set aside.
Scoop 8 equal-sized balls (about 2 tablespoons [45g]) of chilled cookie dough and roll into balls. Once the air fryer is preheated, line the air fryer basket with the prepared parchment paper and place 3-4 dough balls (depending on the size of your air fryer), spaced 4 inches (10cm) apart, and flatten them until ½ inch (1.3cm) thick. Bake for 5-7 minutes, or until they are lightly browned, puffed, and ripped on top.
Remove the air fryer basket from the air fryer and let them cool for 5 minutes in the air fryer basket or until firm enough to move them. Then, transfer to a wire rack and let cool completely. Store in an airtight container at room temperature for up to 3 days or freeze for up to 3 months.