Preheat an air fryer to 375 degrees F (190 degrees C). Grease and flour four 4-ounce ramekins.

Microwave chocolate chips and butter in a microwave-safe bowl on high for 1 minute. Stir and microwave at 15-second intervals until almost melted. Remove from the microwave and stir until completely melted and thoroughly combined.

Add powdered sugar, eggs, egg yolks, and vanilla extract to the melted chocolate; whisk until combined. Add flour and mix until incorporated. Pour batter into the prepared ramekins and place into the air fryer basket.

Cook in the preheated air fryer until edges of cakes are set, 10 to 14 minutes; do not overcook.

Remove from the oven and let sit for 5 minutes. Invert onto dessert plates and serve immediately.