Mix the eggs with the salt and pepper and beat well to combine.
Heat up a frying pan with the olive oil until hot, then turn the heat down to medium to low, pour in the egg mixture, sprinkle a tablespoon of the grated cheese on top of the eggs then place the tortilla over the egg and mozzarella. Let it cook for a couple of minutes until you see the egg starts to thicken, then flip the egg tortilla over and let the tortilla cook for a minute or so. Add the slices of avocado and the rest of the cheese and fold the tortilla in half.
Remove from the heat and serve with some fresh greens, some cherry tomatoes, and low-fat dressing.