Cut the broccoli into small, even florets and place them in a heatproof bowl, discarding any very tough, woody stem pieces.
Pour enough freshly boiled water over the broccoli to cover it completely, then leave it to sit for about 10 minutes so it softens slightly.
Drain the broccoli thoroughly in a colander, then transfer it to a plate or tray and pat it dry carefully with paper towels.
Line the air fryer basket with a piece of parchment paper and lightly brush it with 1–2 tablespoons of vegetable oil, making sure the base is evenly coated.
In a mixing bowl, crack in the three eggs, then add salt and black pepper to taste and beat with a fork or whisk until the mixture is smooth and slightly frothy.
Add the well‑drained, dried broccoli florets to the bowl of beaten eggs and gently stir until every piece of broccoli is coated in the seasoned egg mixture.
Pour the broccoli and egg mixture into the prepared air fryer basket, using a spatula to scrape out the bowl and spread the mixture into an even layer.
Sprinkle the shredded mozzarella evenly over the top of the broccoli and egg mixture, covering as much of the surface as possible with a thin, even layer.
Place the basket into the air fryer and cook at 180°C / 350°F for about 10 minutes, or until the eggs are fully set and the cheese is melted and lightly golden.
Carefully remove the basket from the air fryer and let the bake cool for 1–2 minutes, then lift it out using the parchment, slice into portions and serve warm.