Finely chop the spring onions (green part too) and thinly slice the mushrooms.
Heat the vegetable oil and gently stir-fry the mushroom and onion for a couple of minutes until soft but still have a bite.
In a small bowl, lightly whisk the eggs with half of the sesame seeds.
Transfer the mushrooms to a plate and wipe out the pan. Heat the sesame oil and pour in the egg mixture, allowing it to spread out evenly.
Using a flat wooden spoon or chopsticks, pull the edges of the omelette into the middle, tilting the pan to allow the liquid egg to spread around. Keep doing this until you get a fluffy omelette, which is almost set. Add the mushroom and spring onion mixture to one half of the omelette and scatter the seeds on the other side.
Turn the seeded part over the mushroom half, cook for a minute to combine, then slide it onto a plate.
Serve warm.