Heat butter and olive oil in a pan over low heat.
Add the julienned onion and sliced mushrooms.
Cover with a lid and cook until soft, stirring occasionally.
Season with salt and black pepper.
Pour the beaten eggs over the onion and mushroom mixture.
Sprinkle the chopped parsley on top.
Place the tortilla wrap over the eggs and cover the pan with a lid.
Once the eggs are set, carefully flip everything so the tortilla is now on the bottom.
Sprinkle grated mozzarella and a few parsley leaves on top.
Fold the wrap in half and let it cook for another minute until the cheese melts.
Remove from the pan and serve warm.