Grease a 6-inch, 7-inch, or 8x8 cake pan thoroughly, including the sides.
Spread the dry chocolate cake mix in an even layer across the bottom of the pan.
Sprinkle the dry instant pudding mix evenly over the cake mix.
Whisk the melted butter into the milk, then pour slowly and evenly over the dry layers.
Stir gently until no dry powder remains. Do not mix smooth.
Scatter the chocolate chips over the top.
Place the pan in the air fryer basket. Cook at 310°F for 15 to 20 minutes, checking at 15.
The cake is done when the top is set and a toothpick inserted an inch from the edge comes out with moist crumbs. The center will remain soft.
Rest 10 minutes before serving.