Sauté white onions in 1 tablespoon virgin olive oil in a small skillet over medium heat until translucent and tender. Remove from pan and set aside.
Lightly beat eggs and add to the same skillet. Allow to form bubbles then carefully flip over. Spread cheese and onions over half the surface. Cook for 1 minute more, fold other side over onions and cheese. Cook 1 more minute.
Slide off skillet and on to plate. Season to taste with salt and freshly ground black pepper.