Preheat an air fryer to 350 degrees F (175 degrees C) according to manufacturer's instructions. Spray the air fryer basket with nonstick cooking spray.
Mix oatmeal, flour, cocoa powder, pudding mix, baking soda, and salt together in a bowl until well combined. Set aside.
Cream butter, brown sugar, and white sugar together in another bowl using an electric mixer. Add eggs and vanilla extract. Add oatmeal mixture and mix well. Stir in chocolate chips and walnuts.
Drop dough into the air fryer using a large cookie scoop; flatten out and leave about 1 inch between each cookie.
Cook until lightly browned, 6 to 10 minutes. Cool on a wire rack before serving.