Finely chop the spring onions and slice the bigger mushrooms.
Heat the vegetable oil and gently stir-fry the mushroom and spring onion for a couple of minutes until soft but still have a bite. Add the soy sauce and lime juice, then reduce the sauce.
In a small bowl, lightly whisk the eggs with a few pinches of sesame seeds and the sesame oil.
Pour the egg mixture over the mushrooms, letting it spread out evenly.
Cook for a couple of minutes over medium heat, then put a lid on and cook for about 10 minutes, until the surface is no longer jelly-like. Alternatively, put the frying pan in a preheated oven/grill, and brown the top.
Transfer the frittata to a plate, then cut it into wedges. Alternatively, let it cool and cut it into bite-sized squares.