In a bowl, beat the eggs with salt and pepper.
Heat the vegetable oil in a non-stick skillet over medium heat.
Add the chicken breast and cook until browned and cooked through, about 5 minutes.
Remove the chicken from the skillet and set aside.
Add the mushrooms to the skillet and cook until tender, about 3 minutes.
Add the green onions and cook for another minute.
Return the chicken to the skillet and add the soy sauce and mirin.
Cook for 2 minutes, stirring occasionally.
Pour the beaten eggs over the chicken and mushrooms in the skillet.
Cook until the eggs are set, about 3-4 minutes.
Carefully flip the omelette and cook for another 2 minutes.
Slide the omelette onto a plate and cut into wedges.
Serve hot and enjoy!