In a nonstick pan, we add half a tablespoon of oil and heat over medium heat. When hot, we add the mushrooms. We stir occasionally, cooking until browned and tender. We season with salt and pepper and add the spinach.
In separate bowls, we ready the eggs. Each bowl has 2½ eggs, keeping track of which has the extra yolks and which has the extra whites. Our family has a preference for one or the other, otherwise we could have beat the two extra eggs and divided them amongst the four bowls. We add salt and freshly ground pepper to the bowls. We also have ready the sliced mozzarella.
We set the hot spinach-mushroom filling aside on a clean plate and add half a tablespoon of the oil to the pan. When the oil is hot, we whisk one bowl of eggs well and pour into the pan.
Using a rubber spatula, we push the cooked egg toward the center of the pan until the eggs start to set. When the eggs are almost set, we add a quarter of the spinach-mushroom mixture and a quarter of the cheese. We fold the omelet in half, pull the pan off the heat, and wait about 30 seconds for the omelet to finish setting up.
Then we slide the omelet to the edge of the pan, and turn the omelet out onto a warmed serving plate. We repeat this for the remaining omelets and serve with additional salt and pepper.