Preheat: Set the air fryer to 350°F (180°C) and preheat for 3 minutes. Lightly grease a 6-inch oven-safe pan with cooking spray or butter.
Whisk the eggs: In a small mixing bowl, whisk together the eggs, heavy cream, salt, and pepper for 30 seconds, until the mixture is frothy with visible air bubbles.
First cook: Pour the egg mixture into the prepared pan. Place the pan in the preheated air fryer basket. Air fry at 350°F for 4 minutes.
Add cheese: Sprinkle the shredded cheddar evenly over the partially cooked omelette. Add any optional fillings now (cooked meats, sautéed veggies, fresh herbs).
Finish cooking: Air fry for another 4 minutes at 350°F, until the cheese is fully melted and the eggs are set but still tender.
Serve: Run a silicone spatula around the edges to release. Slide the omelette onto a plate, fold in half, and serve immediately.